A Conversation with Pranab Kumar Sen

Statistic al Scienc e 2008, V ol. 23 , N o. 4, 548– 564 DOI: 10.1214 /08-STS255 c  Institute of Mathematical Statistics , 2008 A Conversation with Pranab Kuma r Sen Mala y Ghosh and Michael J. Schell Abstr act. Pranab Kumar Sen w as b orn on No v em b er 7, 1937 in Cal- cutta, India. His father died when Pranab w as 10 y ears old, so his mother raised the family of seven children. Give n his su p erior p erfor- mance on an exam, Pranab nearly w ent int o medical sc ho ol, but did not b ecause he w as und erage. He receiv ed a B.Sc. degree in 1955 and an M.Sc. degree in 19 57 in statistic s from Calcutta Unive rsit y , topping the class b oth times. Dr. Sen’s dissertation on order statistics and non- parametrics, under th e d irection of Professor Hari K ink ar Nandi, w as completed in 1961. After teac hing f or three y ears at Calcutta Univ er- sit y , 1961– 1964, Professor Sen came to Berk eley as a Visiting Assistan t Professor in 1964. In 1965, he joined the Departmen ts of S tatisti cs and Biostat istics at th e Universit y of North Carolina at Chap el Hill, where he h as remained. Professor S en ’s pioneering contributions ha v e touc hed n early ev ery area of statistic s. He is the first p erson who, in join t collab oration with Professor S. K. Chatterjee, d ev elop ed m ultiv ariate rank tests as we ll as time-sequen tial nonparametric met ho ds. He is also the fi r st p erson wh o carried out in -depth researc h in sequential nonp arametrics culminating in h is no w famous Wiley b o ok Se que ntial Nonp ar ametrics: Invaria nc e Principles and Statistic al Infer enc e and S IAM monograph. Pr ofessor Sen has ov er 600 r esearch publications. In add ition, he has authored or co-a uthored 11 b o oks and monographs, and has edited or co-edited 11 more vo lumes. He has sup ervised o v er 80 Ph.D. students, man y of whom h a v e ac h iev ed distinction b oth nationally and int ernationally . Professor S en is the found in g co-editor of t wo int ernational journals: Se quential Ana lysis and Statis tics and De cisions . He is a F ello w of the American Stati stical Asso ciation and of th e Institute of Mat hematical Statistics, and an electe d memb er of the I n ternational S tatistic al In- stitute. Professor Sen was the third recipien t of the p restigious Senior No ether Award offered by the Nonparametrics Section of the American Statistica l Ass o ciatio n. In 2007, a F estschrift was h eld in his h onor at the Nonparametrics Conference on the 70th anniv ersary of his birth. This con ve rsation to ok p lace at the S p eec h Communicat ion Cen ter, Univ ersit y of North C arolina at Chap el Hill on No ve mber 11, 2005. Malay Gh osh is Distinguishe d Pr ofessor, University of Florida , Dep artment of Statistics, P.O. Box 11 8545, Gainesvil le, Florid a 32611-8545 , USA e-mail: ghoshm@stat.ufl.e du . Michae l J. Schel l is Pr ofessor and Biostatistics Dep artment Ch air, Moffitt Canc er Center, MRC /BIOST A T, 12 902 Magnolia D rive, T amp a, Florida , USA e-mail: michael.sche l l@moffitt.or g . This is an electronic reprint of the o riginal a r ticle published by the Institute of Ma thematical Statistics in Statistic al Scienc e , 2 008, V ol. 23, No. 4 , 54 8–564 . This reprint differs from the or ig inal in pagination a nd t yp ogr aphic detail. 1 2 M. GHO SH AND M. J. SCHELL Fig. 1. Pr anab Sen at age 5. EARL Y YEARS AND COLLEGE D A Y S Sc hell: Go o d mornin g, Dr. Sen. T o b egin our con- v ersation, tell us a b it ab out your early childhoo d y ears. Sen: W ell, I really appreciate this o ccasion to con- v erse wit h b oth of y ou, Mala y and Mic hael. The whole ev ent of life is full of unforeseen and un ac- coun table happ enings starting with birth, p ropagat- ing all the wa y unt il someone closes the eyes forev er. In my case, I w as b orn in a not to o affluen t bu t ed- ucated family; m y father w as a railwa y office r; my mother w as the daughter of a noted ph ysician in herbal medicine, and the pre-secondary school da ys w en t out p rett y smo othly unti l I was ab out 10 ye ars old when m y 43-y ear-old father died of leuk emia, the first detected case in India. Th at w as the first significan t sto chast ic ev en t in m y life and it con- tin ued to hav e a delete rious impact for y ears. My mother, gifted with enorm ous patience, was thrust with the respon s ib ilit y of raising sev en c hildren. I w as the second one, and m uc h later I could appre- ciate ho w diligen tly she hand led the whole matter. When I was in h igh sc ho ol I almost ga v e up m y studies; I wa s ve ry restless and more inv olv ed with sp orts and o ther d istractiv e so cial ev en ts. Gradu- ally , m y mother led me through those difficult da ys unt il I ent ered my final sc ho ol y ear. In my sc h o ol da ys, I nev er had a top standing, u n til in the ten th grade, against all exp ectations, I topp ed the school list in the ann ual as w ell as in the matriculation examinations; in deed a c hancy ev en t b eyo nd my ex- p ectation, the only deterministic factor b eing m y mother’s strong pur suance. Ghosh: Y ou talk ab out y our life in p o etry as one filled with c hancy ev ents (y our verse “My Chancy Life as a Statistici an” repro du ced i n “ Pr anab K u mar Sen : Life and Works ” by Balakrishnan, P ena and Silv apulle, 2008 ); please tell u s ab out some that led y ou to b ecome a statistici an. Sen: When I wa s in the high school, m y mother, based on her (Ayurv edic physic ian) father’s earnest desire, w as hoping all the time that I could go to medical sc ho ol. With that inte ntio n, I w as adm itted to the Int ermediate Science Secti on in R. G. Kar Medical College in Calcutta; the p rincipal, r ealizing m y fi nancial difficulties, told me that if I could se- cure the top score among all studen ts in m y class, I would b e give n a full 5-y ear schol arship to study medicine. I wa s deligh ted with that c hallenging of- fer whic h made me more serious in m y stud ies. An- other c hancy ev ent—when the examinations w ere o v er and I w as ab out to app ly formally and confi- den tly for admission to the medical college, they re- alized that I was 18 months u nderage. I was advised to pu rsue a t w o-y ear B.Sc. d egree and then return to the med ical program; the schola rship b ased on m y earlier examination p erformance w ould remain in- tact. But my un cle advised me to not tak e that risk b ecause if he d ied in the middle of my anti cipated and circumstantia lly en h anced 7 y ears medical stud- ies, I w ould ha v e to quit (without a formal medical degree) and tak e some clerical job to supp ort m y brothers and sisters who were still in sc ho ol. So I had to withdra w myself from that p ossibilit y . I ap- plied for admission and w as selected in to b oth the Mathematic s and Physic s honors pr ograms in the Presidency College, Calcutta. Another casting of a die: Prabir Ac hary a, a s c ho ol friend of mine, came to see me then and suggested that I not tak e any one of them b ut rather nego tiate for S tatistic s hon- ors where I c ould do ev en b etter. I c onvince d m y mother and uncle and switc hed to Statistics honors in the s ame college ; that brought me to statistics in the fi rst place whic h I w asn’t at all planning. Ghosh: Wh at did y ou th in k ab out statistics, once y ou en tered the pr ogram? Sen: I started app r eciating more and more this no v el discipline during m y undergraduate y ears in A CON V ERSA TION WITH PRANA B KUMAR SEN 3 the Presidency C ollege and sub sequen tly at the Cal- cutta Unive rsity , lo cated just across the street from the Presidency C ollege . W e had w onderful and most dedicated teac hers in b oth places. Professor Anil Bhattac harya, a well-kno wn statistician (famous for the Bhattac harya inform ation b ound and dive rgence measure), w as our teac her at the Presidency College. Professors B. N. Gh osh and P . K. Banerjee taugh t us at b oth the Presidency College and the Universit y , while P rofessors P . K. Bose, M. N. Ghosh, H. K. Nandi, K . N. Bhattac hary a, K. C. Seal and others taugh t us at the Un iv ersit y . They had tremendous insigh t and had a profound impact on m y p ercep- tions, int erest and career dev elopmen t in statistics. My uncle urged me not to pursue the Masters degree after completing the B.Sc. honors program, b ut to tak e a job to su pp ort my br others’ and sisters’ ed- ucations (as in my elder brother’s case). But, as I did w ell in my B.Sc. h onors p r ogram, I was giv en the signal to go for t wo more y ears in the M.Sc. program. There to o I did we ll, but my family’s fi- nancial situation led me to seek a job. I w en t to the Indian Statisti cal Institute, Calcutt a (IS I), hoping for an assistan tship that could enable me to pursu e a do ctoral degree w hile providing financial sup p ort to m y family . I was intervie wed and aptitude tested at ISI but w as not selected. I w as advised to tak e a regular administrativ e job in the Demograph y (Vi- tal Statistics) Departmen t with the Go v ernment of W est Bengal. I r ealize d, though, that alt hough that job migh t well satisfy my financial needs, it would not lead to my career ob jectiv es. T hus, I came bac k to m y alma mater, Calcutta Univ ersit y Statistics Cen ter and was most heartily welco med b y all my teac hers there. Because of the u sual irregularit y of receipt of stip end, I to ok some extra tutorial jobs to supp ort m y sib lings’ educations. Professors Manin- dra Nath Ghosh and Hari Kink ar Nandi w ere the t w o teac hers who supp orted me most in this v en ture. Professor Ghosh left for another academic p osition in the In s titute of Agricultural Researc h Statistics, New Delhi, just b efore our M.Sc. examinations w ere o v er, but he ke pt a vigilan t ey e on m e and con tinued in teracting when needed. I w as really fortunate to ha v e Pr ofessor Hari Kink ar Nandi as my advisor, guru and men tor for four y ears whic h I c herished most d eeply; I co uld visualize a broader int erpretation of the sub ject, b ey ond the fenced domain of mathematical statistics and p r ob- abilit y theory , and it broadened my interest in such Fig. 2. While i n Pr esidency C ol l e ge, Calcutta, 1954. a profound wa y that, ev en after earning a Ph.D. de- gree, I con tinued to ha v e an appreciation of s tatis- tics encompassing its in terdisciplinary applications as well as statistica l theory . Ghosh: In teresting. Ob viously Professor Hari Kink ar Nandi h ad a clear impact on you, and m an y of us were his studen ts also; can you tell us more ab out him, his men torship of yo u, and his st yle? Sen: He did not hold a formal Ph .D. degree in Statistics or an allied sub ject bu t w as the top ment or for ab out 20 do ctoral students, many of whom h a v e done extremely w ell. He wa s the founding editor of the Calcutta Statistic al Asso ciation Bul letin , and with dedicat ion and distinction, he edited the j our - nal for ab out 30 y ears. Although I was formally his first ad visee, at least four others b efore me w orke d under his sup ervision, alb eit unofficially . I w as for- tunate to ha v e strong friendships with t wo fello w studen ts, Shoutir Kishore Chatterjee an d J ay anta Kumar Ghosh. W e us ed to sit in a small ro om w ith barely the leg space for three small d esks and n oth- ing else. Library and computing facilities w ere in- adequate, but not our m orale; our strength was our men tor Pr ofessor Nand i and the unique envi ronment created w ithin the w alls of those small ro oms con- stituting the first Statistics department in India. W e w ere giv en a complete free hand to c ho ose our o wn 4 M. GHO SH AND M. J. SCHELL Fig. 3. Jayar am Sethur aman, Madan and Uma Puri, Chuck Bel l, Pr anab Sen and Shoutir Chatterje e at the first Nonp ar a- metrics Confer enc e, Blo omi ngton, IN, 1969. dissertation topics but with helpfu l hands wh enev er w e n eeded. I could appreciate how that help ed us de- v elop the spirit of appraising cont emp orary researc h with a view to exploring further w ork. Professor Nandi was a bac helor. In his und ergrad- uate class, he did v ery w ell in Physic s Honours, and he mov ed to Statistics at the Masters lev el. Design and analysis of exp erimen ts, multiv ariate analysis, sample surve y and statistical inference (including decision theory) were his primary areas of in terest, although h e had pr ofound knowle dge in m an y other fields. What caused me the most w onder wa s that he Fig. 4. Bikas Si nha, Pr anab and Gauri Sen, Mrs. and Dr. A. K. Md. E Saleh, J. K. Ghos h and Mrs. and Dr. A. P. Basu ar ound a r estaur ant ta ble in Cair o, 1991. A CON V ERSA TION WITH PRANA B KUMAR SEN 5 Fig. 5. Julio Singer, John Pr eisser, Antonio Pe dr oso de Lima and Pr anab Sen in the M cGavr an–Gr e enb er g Building c ourt- yar d, 1994. suggested dive rse areas of researc h to his advisees so that w e would eac h feel comfortable wo rking in our area of sp ecializations. This trend con tinued with his later advisees to o, including S. R. Chakrab orti, Fig. 6. Kim, Gauri, Pr anab, Devi, Ru and Joy (standing) at home i n Chap el Hi l l, 1997. 6 M. GHO SH AND M. J. SCHELL Fig. 7. Malay Ghosh r aises a question for Pr anab Sen as the 2002 No ether Awar d sp e aker, Joint Statistic al Me etings, New Y ork City. Basudeb Adh ik ari, Arijit Chaud h uri and Bimal and Bik as Sinha (the s tatistical t wins). A few y ears af- ter joining Calcutta Univ ersit y , he started studying homeopathic and b io c hemical medicine on his o wn . W e used to wo nd er how detac hed a p erson could b e and still h ow devo ted was he to the adv ancemen t of p ostgraduate training and researc h in sta tistics in the Indian sub con tinen t. It was ind eed a golden op- p ortunity for us to app reciate his wisdom, p atience and men torship. Fig. 8. Pr anab Sen and Ra lph D’A gostino at the No ether L e ctur e, Joint Statistic al Me etings, 2002. A CON V ERSA TION WITH PRANA B KUMAR SEN 7 Fig. 9. Gauri and Pr anab in Alaska, 2002. RESEARCH A T CALC UTT A UNIVERSITY Ghosh: T ell u s a b it ab out your researc h at Cal- cutta Un iv ersit y . Sen: As I started tea c hing in Calcutta Univ ersit y in 1961, I w as ask ed to teac h a course on Biologi- cal Assay . I r ealized at that time that full atten tion w as b eing paid to only the normal tolerance dis- tribution. I though t that that w as v ery unrealistic b ecause, in most ca ses, tolerance distributions were v ery skew ed, and ev en after suitable d osage transfor- mation, were not near to n ormal ones. My next sis- ter, Mala y a, in her d issertation work in ph ysiology , had a lot of data from Calcutta Medical S chool on triglycerides and other blo o d c hemicals; their d istri- butions b eing hea vily ske wed. I observ ed that even after log transf orm ations, near-normalit y wa s not ac hiev ed. This inspired me to dev elop nonparamet- ric m etho ds for biologica l assa ys. The 1963 Biomet- rics pap er (Sen, 1963a ) w as probably the v ery first Fig. 10. Shoutir Chatterje e, Pr anab Sen and Jayanta Ghosh, Kolkata, India, 2003. 8 M. GHO SH AND M. J. SCHELL Fig. 11. Pr anab Sen at his offic e i n Chap el Hil l, 2007. nonparametric one in bioassa y . I observe d that b e- cause ranks are inv arian t under arb itrary strictly monotone transformations, an estimator of the rela- Fig. 12. Malay Ghosh, Pr anab Sen and M ichael Schel l at the 70th Bi rthday F estschrift for Pr anab Kumar Sen, annual Nonp ar ametrics Confer enc e, Col umbia, SC, 2007. tiv e p otency based on the ranks (viz. the Wilco xon– Mann–Whitney statistic) wo uld enjo y the same prop- ert y; that is, it w ould not matter whether w e work ed with the log of the dose, or an y other transforma- tion. Th is inv ariance eliminates all the arb itrariness of dosages that underlies th e use of the conv ent ional normal tolerance distribution. After completing m y Ph .D. w ork in order statis- tics and nonp arametrics, I was lo oking for new f ron- tiers of researc h. I conv erged with Shoutir Chatter- jee to a common d omain: multiv ariate analysis from his exp ertise and nonparametrics f r om mine! The whole area of m ultiv ariate nonparametric anal ysis flourished in Calcutta in 1963 (Sen, 1963b ); and our first p ap er (Chatterjee and Sen, 1964 ) on biv ariate t w o-sample lo cation problems, some 40 pages long, pro vided all the imp etus to prob e in to this fertile area in subsequent y ears. I w as also able to extend th e find ings of my 1960 U-statisti cs pap er (Sen, 1960 ) to dep enden t sequ en ces arising in time series mo dels, and with the help of Professor Nandi to finite p opulation sampling (Nandi and Sen, 1963 ), the latter b eing the v ery first w ork on the theory of U-statistics in fin ite p opulation sampling. Ev en n o w I see some p eople using suc h results in complex sampling sc h emes, surviv al anal- ysis and time series anal ysis. Sc hell: In 1964 y ou left In dia to tak e a visiting professorship at Berkel ey . W as th at a difficult step to ta ke ? Sen: It wa s less difficult in 1964 than t wo y ears ear- lier wh en I was offered exactly the same p osition b ut could not come partly d u e to family resp onsib ilities. By 1964 m y sister Mala ya had earned her Ph.D. d e- gree in ph ysiology and brother Mander complete d his engineering degree. A sho wer of c hances: I got three offers within a span of a we ek: one fr om the Lehigh Univ ersit y in Bethlehem, P ennsylv ania, the second f r om the Un iv ersit y of California, Berk eley , and the third from Universit y of North Carolina, Chap el Hill. The UNC offer w as largely due to M. N. Ghosh’s effort; actually , I learned later on that he was offered a senior p osition at UNC b ut could not come, and he recommended me strongly to Dr. Green b erg. I recall that Pr ofessor S. N. Ro y , the guru of our gurus and a most resp ected professor at UNC, while visiting Calcutta in the fall of 1962, b ecame a ware of my offer from Berk eley , and also w an ted me to come to Chap el Hill to work with him. All forces united b ehind the Ch ap el Hill offer in 1964. Ho we ve r, the we ek b efore the UNC offer, A CON V ERSA TION WITH PRANA B KUMAR SEN 9 I w as offered a one-y ear visiting p osition by Profes- sor Lu cien LeCam from Berke ley , which I accepted promptly . I inform ed Professor Greenberg of m y ac- ceptance of the Berke ley offer, and he replied: “No problem. Go to Berk eley and we will snatc h y ou from there n ext y ear.” And that is exactly ho w I came to Chap el Hill in 1965. W as it n ot a c hancy outcome? MO VE TO CHAPEL HILL Sc hell: Y ou came to Chap el Hill in the fall of 1965 , whic h is 40 ye ars ago, and you obvio usly ha ve lo v ed it here b ecause yo u are still here at UNC, so the random w alk of y our life seemed to slo w d own a bit. Sen: It is in a sense true but ev en after coming here, I had not decided whether I should sta y for a long time or should go bac k to Calcutta. I r emem- b er durin g the three ye ars (1964–196 7) when I w as on lea v e of absence f rom Calcutta Unive rsity , I used to write my b oth affiliations on all m y publicatio ns. Some of my Chap el Hill collea gues used to ask me whether I wa s serious ab out con tin uing th is dual af- filiation! I had to defend m yself—Calcutta Univ er- sit y was my home and I couldn ’t give it u p . Even tu- ally , I realized th at UNC wa s one of the b est places for statisti cs in America, if not the w orld, and b y b e- ing here I could not only strengthen m y backg round but d ev elop additional ties with Indian schools. This w a y UNC induced me to settle in C hap el Hill, de- spite several offers fr om other univ ersities o v er the y ears. Before 1964, my attra ctions for UNC were mostly due to Professors Hotelling, Ho effding, John- son and Roy in the Statistics Departmen t and Green- b erg in Biostatistics. Since Professor S. N. Ro y passed a w a y in 1964 b efore my arriv al in Chap el Hill, I re- alized that I could reviv e my researc h in terest on order statistics here with Johnson, Greenb erg and H. A. Da vid , who came a year earlier. My aspira- tion was to strengthen my mathematics bac kground and at the same time dip into the high-tides of ap- plications which wo uld mak e th e statistical researc h relev an t. Sc hell: T ell me ab out s ome of y our early researc h efforts. Sen: As I said earlier, it wa s v ery nice of Professor Nandi to let us choose our own dissertation topics. In the course of this searc h, I came across a pap er of Hotelling and Chu on the m oments of the sample median (Ch u and Hotelling, 1955 ). I could see that their fi nding could b e extended to a general class of sample quan tiles; that led to a 1959 pap er of min e (Sen, 1959 ) wh ich constituted the first part of m y dissertation. I also came across a classical pap er on the theory of U-statistics b y Professor W assily Ho- effding. I extended the results and wrote a pap er whic h o ccupied another ma jor part of my disserta- tion wo rk and w as p u blished in 1960 (Sen, 1960 ). This pap er con tained all the basics of a v ariance estimatio n tec hn iqu e now kno wn as the jac kknifi n g v ariance estimator. Dr. W. J. (Jac k) Hall, who wa s also at Chap el Hill at that time, b rough t it to the atten tion of other researc hers. Professor Ho effding got inte rested in this wo rk and wrote a UNC tec hni- cal r ep ort in 1961 (Hoeffding, 1961 ), wh ere he men- tioned that Sen had considered the result under a momen t condition of ord er greater than 1 while he w an ted to pro v e the r esu lt assuming only the first momen t. He used an ingenious martingale metho d, but got stuc k at some p oint and was so absorb ed in other things that he left it un finished. In the mean while, Bob Berk ( 1966 ) considered a rev ersed martingale approac h in a different con text, yield- ing as a b ypro duct the almost su re conv ergence of U-statisti cs und er the first momen t. Th is martin- gale theory for U- statistics reshap ed the study of asymptotics not only for U-statistic s but also for general nonparametric statistics. Most of these d e- v elopmen ts as w ell as extensions of my 1963 b ioas- sa y pap er (Sen, 1963a ) to ok place after I came to Chap el Hill, and th at left m e with a d eep sense of satisfactio n. All th ese con vinced me to make Chap el Hill m y second home; actually , my wife and I hav e sp ent more time here than anywhere else! F AMIL Y Sc hell: V ery inte resting. Y our family flour ished when y ou came to Ch ap el Hill; tell us more ab out y our wife, Gauri, and y our c hildren, Dev adutta and Anir u d- dha. Sen: W e got married in 1963. Gauri came from a more affluen t family; her father w as an outstand- ing man in m any resp ects, a science graduate with an int erest in managemen t. A t that time I w or- ried ho w her family b ac kground could matc h with mine. No w, without hesitation, I could say that sh e w as very adaptiv e. My birth famil y liv ed with all m y uncles and a unts to gether, some 30 p eople in a household. Her p aren ts and m y mother arranged for the negotiat ed marriage; I fir st saw h er on our w edding da y . My mother was so happy to see this y oung d aughter-in-la w from a very differen t family 10 M. GHO SH AND M. J. SCHELL Fig. 13. Pr anab Sen, Jana Jur e´ ckov´ a and Gauri Sen at the 70th Annivers ary F estschrift for Pr anab Kumar Sen, Columbia, SC, 2007. bac kground adapt well in our household. After com- ing to Ch ap el Hil l, I could see that if I sta yed, I w ould need the maxim u m supp ort from her—and it still con tin ues—but how wonderful she has b een all these y ears, n ot only supp orting me bu t fulfilling the d reams of my mother. Our t w o c hildren, Dev adutta (d augh ter) and Aniruddh a (son), w ere b orn in Chap el Hill in Octo- b er 1966 and F ebruary 1973, r esp ectiv ely . Devi ma- jored in Journalism at UNC, and wo rked for n ews- pap ers in F ort My ers, Florida, and Danvill e, Illinois, and Atla nta (the Constitution). She is pr esently pur - suing creativ e w r iting at home while r aising h er three activ e c hildr en. Our son, called Ru b y h is friends, ma jored in S p eec h Comm u nication at UNC. Dur- ing his studies he b ecame v ery strongly r eligiously minded and now he is a minister in a Presbyt erian c h urch here. He has a son, Jacob K aly an, b earing our family name, and a daughter, Lily . W e are ve ry happy with b oth our c hildren and all our grandchil- dren, to o. MAJOR CAREER A COMPLISHMENTS Ghosh: W e tal ke d ab out y our career working on all the statistic s and nonparametrics. F rom a cita- tion p ersp ectiv e, yo ur p eak y ears o ccurr ed in the y ears 1966–1 975. Articles that you wrote during those 10 y ears ha ve receiv ed more than 1, 000 citations. Can y ou tell us about y our w ork in these y ears? Sen: Y ou kno w, Mala y , I am not that citation minded and h a v e nev er paid an y atten tion to cita- tions b ecause I hav e the con viction that creativit y and citatio ns are t w o differen t attributes; com bining the t w o needs a sp ecial talen t, and I confess th at I am n o go o d in that p ersp ectiv e. T he curr en t fash- ion of coun ting citations often ov erlo oks the early dev elopmen ts. Is it n ot tru e th at the citation bu s i- ness flourished in the 198 0s, and hence pu b licatio ns prior to 1970 hav e often b een p u t in the bac kburn er! Just to emphasize this p oin t let me men tion the I SI citatio n in mathemati cal scie nces cov ering the p e- rio d 1991–200 0; you will see that out of more than 200 top citations, although some 80 are from the statistic s area, they did not include the pioneers whose fundament al con tributions in the 1950s and 1960s reshap ed the statistics discipline. Indeed cita- tion scoring is a d ifferen t kind of game. Ghosh: I kno w that y ou don’t care ab out citatio ns, but I still like to dra w atten tion to one of y our non- parametric pap ers, Estimates of the Reg ression Co- efficien t based on Kend all’s T au (Sen, 1968 ). This pap er has receiv ed nearly 250 c itations (386 as of A CON V ERSA TION WITH PRANA B KUMAR SEN 11 Marc h 2009). T he inte resting thing is the pro cedur e that you describ e has now b ecome kno wn as the Sen–Theil Approac h. What made you think ab out this p ro cedure? Sen: W ell, that pap er was generated f rom m y 1963 Biometrics pap er (Sen, 1963a ) whic h d ealt with the t w o-sample p roblem; I wa s con vinced that some- thing true for the t wo-sample case m ust b e ca pable of yielding a similar picture for the simple regres- sion pr oblem. When I lo ok ed at Kendall’s T au and its inv ariance under any strictly monotone trans f or- mation on the observ ations, I said to myself: “This is wonderful, b ecause all the enti ties in this statistic are the signs of the divided d ifference of pairs of ob- serv ations and their r egressors!” Th erefore, the same structure exploited in the Wilco xon tw o-sample case can b e u sed here. It app eared that the sample me- dian of these divided differences, yielding the p oin t estimate of the slop e, reduces to the estimate of the shift in the t w o-sample case. F u rther, th e d istribution- free confidence in terv al in the tw o-sample case ob- tained in 1963 go es o v er smoothly for the simple r e- gression mo del. A t the same time, this s imp le c har- acteriza tion do es n ot hold in general for estimates based on general linear rank statistic s, ev en in the t w o-sample mo del. There is a need for iterativ e so- lutions; that was the ma j or initiativ e. James Adic hie, in 1967, considered estimation of the regression slop e based on linear r ank statistic s (Adic hie, 1967 ). Although his w ork was ve ry inter- esting, he could not come u p with an explicit form of the p oin t estimator n or of a distribu tion-free con- fidence in terv al. H. Theil, an emin ent econometri- cian, had run int o similar problems bu t got some v ery int eresting and motiv ating results, esp ecial ly for the case wh ere the regressors are all distinct. Though not a mathematical sta tistician, Theil re- ally pr ovided a clear-cut direction long b efore my 1963 Biometrics pap er or the cont emp orary work of Ho dges and Lehmann ( 1963 ). Establishing the in- v ariance and other statistic al prop erties (including asymptotic normalit y , consistency , and p ossible ex- tension to measurement err or mo d els), I was able to go one more step in statist ical inte rp retation and ap- plication. I could men tion also that m y 1968 pap er led to some other work by Jana Ju re ´ ck o v´ a ( 1969 ), Hira K oul ( 1969 ) and you and me to o w here some re- fined results on “asymptotic linearit y of rank statis- tics in r egression parameters” w ere dev elop ed and exploited in the study of asymptotic prop erties of estimators (Ghosh and S en, 1971 ). Coming bac k to y our p oint on citatio ns, I h a v e the feeling if the cita- tion we b w ere in effect fr om 1960s, instead of 1980s, the p icture could ha ve b een different! Ghosh: L et me come bac k to yo ur 196 3 Biomet- rics pap er. It is true that y ou hav e indep en d en tly prop osed a n onparametric estimato r of relativ e p o- tency that w as essential ly the same as the rank es- timator of shift parameter considered b y Ho dges and Lehmann ( 1963 ) at the same time, and is com- monly referred to as the Ho dges–Lehmann estima- tor. Should not w e term it as the Ho dges–Lehmann– Sen estima tor? Sen: Again, Mala y , I w on’t go for any p rofound claim, but if y ou and others who know the field well w an t to do so, I won’t raise an y serious ob jection. In h is 1974 Nonp ar ametrics b o ok (Lehmann , 1974 ), Lehmann p oint ed out somewhere that for bioassa y mo dels, Sen ( 1963 a ) considered the same estima- tor. T o bypass this accredita tion problem, some p eo- ple simply refer to that as the Wilco xon score R- estimator. It ma y n ot b e out of the w a y to ment ion that while yo u and others ma y debate on this small p oint , in 1966 Pr ofessor No ether p oint ed out to us a 1952 b o ok chapte r (in W alk er and Lev) b y Lin- coln Moses (Moses, 1953 ), w ho explored the median of midranges of all p ossible distinct pairs, kn o wn as the W alsh median, just a bit d ifferen t from the Wilco xon score estimator, and in 196 5, Dr. Moses pro vided a graph ical display of the Wilco xon score t w o-sample p oin t as we ll as confidence in terv al es- timator (Moses, 1965 ). Thus, p erh aps w e should all share the cake of creditation and resolv e any p oten- tial con tro ve rsies amiably! As a matter of fact , in the 196 7 Join t Statistica l Meetings in W ashington D.C., Gottfried No ether organized an invited pa- p er session w ith Eric h Lehmann and me, and him as the third sp eak er. As Eric h could not come, Pe- ter Bic ke l was his substitute. I talk ed ab out non- parametric co nfi d ence interv als, exploiting m y 196 6 Anna ls pap er (Sen, 1966 ), and going b ey ond to the Kendall T au statistic-based ones. No ether was so in- terested, kn o wing that you were ab out to earn your Ph.D. degree on related topics, h e in vited yo u to his departmen t and offered y ou a f aculty p osition. Ghosh: T hat’s correct. I r emem b er that I p r e- sen ted there some w ork on a sequenti al confi d ence in terv al based on the Kendall T au statistic, and it w as very well receiv ed. I know that y our area of ex- p ertise co vers parametrics, nonparametrics as w ell as semiparametrics wh ic h were yet to b e p opular in the early 1970s. Th ose of us around in Chap el Hill 12 M. GHO SH AND M. J. SCHELL at that time used to regard you as a mathemati - cal statistician, alb eit in residence at a biostatistics departmen t. W e knew that yo u h ad gen uine inter- est in applications, and y et up to that time, yo ur w ork w as p redominan tly in theory and metho dol- ogy , with o ccasional d etours in probabilit y theory and sto c hastic pro cesses. Could you explain what in- spired yo ur transition to more application-orien ted metho dology resea rch? Sen: Mal a y , I wo uld lik e to iterate that the broad training in statistics I had in Ind ia led to my con- viction not to limit m ys elf to narro w sub-areas of mathematica l statisti cs. My in clination to cont inue at UNC was p rimarily in fluenced b y the set up of the S tatistic s Departmen t in the College of Arts and Science and Biosta tistics in the Sc ho ol of Pub- lic Health, within the Division of Health Affairs. I w as giv en a free hand to wo rk in b oth departmen ts and thereb y could appreciate the tremendous s cop e of statistics in the mathematica l as we ll as clinical and p ublic health disciplines. In fact, Dr. Green b erg w as fully a ware of my b ac kground and aspir ation, and made it clear that it w ould b e highly b enefi- cial f or the Biostatistic s Department if I con tin ued w orking with goo d metho dological problems while m y colleagues collab orated on health and clinical re- searc h applicatio ns. This w as the b est opp ortun it y I co uld exp ect at an y place. Professors Jim Grizzle, Rob ert Elston, Gary Ko c h and others w ere more in tensely dev oted to applied work, and I could col- lab orate w ith them whenev er they had any metho d- ologic al problems and there was no d earth of that. Jim Grizzle w as inv olv ed with m essy d ata problems in medica l studies, and had many practical insigh ts whic h needed metho dological supp ort, and this pro- vided the orien tation of m y gro wing inte rest in ap- plied w ork. I recall that Mala y , Jim and I w ork ed out some nonparametrics for growth curv e analysis in the early 1970s wh ic h app eared in the J ournal of the Americ an Statistic al Asso ciation (Ghosh, Griz- zle and Sen, 1973 ). Ghosh: P lease describ e the LIP I DS p ro ject for whic h y ou dev elop ed some inte resting metho ds. Sen: In the f all of 1971, the UNC Biostatist ics and Epidemiology Departments were aw arded a long- term clinical co ordination task b y the National Heart, Lung and Blo o d Institute, called the LIPI DS pr o ject. Eigh t hospitals across the count ry w ere co ordinated for a m ulticen ter longitudinal study of the impact of lo w ering bloo d c holesterol lev el on reduction of car- dio v ascular disease risk. Some 3,952 healt hy males b et we en the ages of 35 and 60 y ears, with c holesterol lev els of 230 or more, were included in a doub le-blind study with t w o groups: placeb o and treatmen t, o f almost equal num b er. Their failure patterns were to b e s tatistically app raised. T h e NIH team had a v ery plausible hyp othesis mingled with m edical ethics and op erational cost constrain ts. The study could b e con tin ued to a maximum of 12 years’ p e- rio d (Ju ly 1972 to June 1984), bu t if at any int er- mediate p oin t of time, the n ull hypothesis of n o d if- ference b et w een the placeb o and treatmen t group w as rejected in fa vor of the treatmen t group, the trial should b e stopp ed with the surviving sub jects switc hed to the treatmen t group; thus the n ull hy- p othesis w ould only b e accepted if th ere w as no comp elling statistical evidence of b etter surviv al for the treatmen t group thr oughou t the study . Since this study inv olve d a common cohort o f sub jects, the time-sequenti al failures were neither indep en- den t n or iden tically distrib u ted. On top of that there w ere many explanatory v ariables so that und erlying failure distribu tions w ere not simple. The cla ssical W ald sequen tial probabilit y r atio test w as deemed inapplicable, and there was righ t-truncation due to the imp osed tw elv e-y ear du ration as wel l as p ossible drop out and n oncompliance. I was ask ed to dev elop the statistical m etho dology for this sequen tial pr o- cedure, with in terim analyses to b e appraised ev ery 3 mon ths. F ortunately Professor Shoutir Ch atterjee from Calcutta w as visiting UNC in 1 972, and to- gether w e dipp ed into the n ature of the sto chastic pro cesses arising in su c h sc hemes, w ithout assum- ing any sp ecific p arametric mo dels. Another chancy ev en t: W e observed that under the null h yp othesis, a general class of linear r ank stat istics has a simple martingale str u cture that can b e incorp orated in a p ermutat ion setup for nonparametric analysis and y et can b e attuned to the W ald sequentia l prob- abilit y ratio test theory by transforming cale nd ar time to information time. This long pap er (Chatter- jee and Sen, 1973 ) pro vided the access to suitable applications in the L I PIDS as well as other clinical trials. Mala y , y ou ma y recall that ma yb e a y ear or t w o later, we wo rked on martingale p rop erties of con- v en tional rank statistic s w ith resp ect to the sample size v ariation. These t w o r elated researc h questions absorb ed me completely for a decade (19 72–1982) . Ghosh: Linking nonparametrics with sequen tial metho ds w ith applicati on to clinica l trials? A CON V ERSA TION WITH PRANA B KUMAR SEN 13 Sen: Y es, with man y advisees, this w ork culmi- nated in Se quential Nonp ar ametrics (Sen, 1981b ). The most app ealing p oin t in this effort w as the ba- sic feature that statistic al metho dology can really op en up a c hain of fruitful applicatio ns in clinical trials, time-sequen tial pro cedu res, rep eated signif- icance tests and sur viv al analysis. Most probably , due to this wo rk, I was end o w ed with a d istinguish ed professorship at UNC in Jan uary 1982 w hen I w as 44 y ears old; also I was designated as NSF/CBMS Lec- turer in Statistics, and pr esen ted a set of 10 lectures on “Theory and Application of Sequen tial Nonpara- metrics” at the Unive rsity of Io w a. This area of re- searc h is now floo ded w ith sta tisticians, going b e- y ond parametrics, and it giv es me great satisfaction to kno w that b ac k in the 1970s th e few of us who w ere pu rsuing metho dological researc h in applied clinical pr oblems we re able to provide the imp etus for ot hers to join the camp. Sc hell: This imp ortan t dev elopmen t o ccurred ab out the same time as the classica l w ork of D. R. Co x ( 1972 ). Could y ou commen t on the impact o f h is w ork on y our s ? Sen: Th is seminal w ork of Da vid Cox w as un- doubtedly a masterpiece; it dev elop ed a prop ortional hazard mo del whic h laid down the foun dation of semiparametrics. Th e b eaut y of this pap er is the mo- tiv ation and general formulat ion. The mathematical foundations were dev elop ed later b y Co x ( 1975 ) and more rigorously by many others in the late 1970s and early 1980s going o ve r to the so-ca lled m ultiplica- tiv e int ensit y pro cesses. With m y own inclinatio n on martingale c h aracterizations of v arious statistics in 1981, I was also able to c haracterize the general asymptotics f or the Cox mo del, through martingales for induced order statistics or concomitan ts of order statistic s (Sen, 1981a ). The pr op ortional hazards as- sumption, basic to the Cox mo d el, needs to b e crit- ically appraised in any real application. Jim Griz- zle and I came across a ca se with the congesti on in the upp er aorta for elderly p eople where some statistic ians we re blindly u sing a p rop ortional haz- ard mo del for the su rgery and medication groups. Ho w ev er, the hazard fun ctions we re qu ite different and crisscrossed; hence, Co x m o del-based analysis w as n ot ideal . T here are count less suc h instances, and I hope that semiparametricia ns who lo ve the Kaplan–Meier estimator (Kaplan and Meier, 1958 ) and the Co x prop ortional hazard mo del for their mathematica l con v enience w ould c hec k the appro- priateness of such simplifying assumptions in their sp ecific conte xts. I had a conv ersation w ith Da vid Co x quite some time ago, and he also ec ho ed sim- ilar sentimen ts. I wish that more of us would ha ve suc h insigh t. Sc hell: Y ou h a v e also done tremend ous w ork on sequen tial analysis and on a mixture of nonpara- metric and sequentia l metho ds. When did you first get intereste d in sequent ial analysis? Sen: In 1958–1 962, Sh ou tir Chatterjee and Jay anta Ghosh w ere b oth w orking on sequen tial metho ds, while I fo cused on nonparametrics. Inte ractions with them initiated my interest in sequen tial method s as w ell, alb eit w ith an ey e on linking it to nonparamet- rics. Ho we ve r, m y activ e in vo lve ment dawned ab out a decade later when Mala y w as a p ostdo c at UNC, and w e launc hed on nonparametric sequent ial meth- o ds in a systematic w a y using martingale theory . This kept me busy durin g 1971–1983. Bac k in 1972, to this sequen tial arena, with ac tiv e collab oration with Ch atterjee, w e w ere able to annex the time- sequen tial analysis based on nonparametrics. Sc hell: One of y our biggest strengths is the use of sophisticated asymp totic theory in vir tu ally ev ery area of statistics. Ho w did y ou dev elop the skill? Sen: Th e thrust for asymptotics started with my dissertation w ork bac k in 1958–195 9. The main in- spiration came from Professor M. N. Ghosh; his asymptotic w ork in the early 1950s on serial rank statistic s drew my int erest but I realized that I w ould need to stren gthen m y mathematical bac kgroun d. The UNC Statistics complex provided me with th e golden opp ortunit y to further this ob jectiv e and again I wo uld also ac kno wledge the tremend ous in- spiration and supp ort I receiv ed fr om Dr. Green- b erg in Biostatisti cs. I extended m y wo rk on func- tional cen tral limit theorems and inv ariance princi- ples for U-statistics as well as rank statistic s with suc h no v el asymptotics. Bac k in 1960, the lev el of asymptotics w as set b y the 194 8 semin al work o f Ho effding on U-sta tistics (Ho effding, 1948 ) and the more recen t work of C h ernoff and Sa v age ( 1958 ) on rank statistic s. The con tiguit y-based approac h in H´ ajek ( 1962 ) set another d irection to this asymp - totics while the Pyk e–Shorac k (Pyk e and Shorac k, 1968a , 1968b ) and H´ ajek ( 1968 ) work led to ad- ditional a ve nues. I w as f ortu n ate to b e abreast of these dev elopmen ts, and using martingale metho d s, w e extended the cont iguit y approac h to a more gen- eral asymptotic setup. These d ev elopmen ts culmi- nated in m y 1981 sequentia l n onparametric b o ok 14 M. GHO SH AND M. J. SCHELL (Sen, 1981b ), bu t are still very m uch relev an t to my metho dological w ork in some applied pr oblems. Ghosh: In addition to y our nearly 600 p u blica- tions, y ou ha v e authored o r co-authored 11 b o oks and monographs, and edited or co-edited 11 more. Ho w did yo u fin d time for these things? Sen: Mala y , I am in the academics for ab out 45 y ears, and these deve lopment s did not tak e place o v ernigh t! I had a mo dest n umber of p ublications prior to mo ving to UNC, but collab oration w ith a large n umb er of collea gues and advisees resulted in this sp ectrum, so my credit h as to b e discount ed ac- cordingly! F rom 1965–1971 , Dr. Green b erg enabled me to dev ote 75% time to researc h, and that re- ally help ed in completing the 1971 b o ok on m ul- tiv ariate nonp arametrics w ith Madan Puri. During the 197 0s, I had littl e time to write monographs. Ho w ev er, b eginning again in the 1980s, I had more opp ortunity to complete Se quential Nonp ar ametrics (1981 , 1985) (Sen, 1981b ), Handb o ok of Statistics, V olume 4: Nonp ar ametric Me tho ds with Dr. Krish- naiah (Kr ishnaiah and Sen, 1984 ), Nonp ar ametric Metho ds in Gener al Line ar Mo dels with Madan Puri (Puri and Sen , 1985 ), and a couple of F estschrifts in honor of Norman Johnson and Bernard Greenberg. The 1990s were more devo ted to b o ok writing: L ar ge Sample Metho ds in Statistics with Julio Singer (Sen and Singer, 199 3 ); Pitman ’s Me asur e of Closeness with Jerr y Keating and Bob Mason (Keating, Mason and Sen, 1993 ); R obust Statistic al Pr o c e dur es with Jana Jure´ ck o v´ a (Jure ´ ck o v´ a and Sen , 1996 ); and Se- quential Estimation with Nitis and y ou (Ghosh, Mu- knopadhy a y and Sen, 1997 ). Bac k in 1994, Mrs. H´ ajek and Professor ˇ Sid´ ak ask ed me to undertak e a thorough r evision of the classic H´ ajek– ˇ Sid´ ak The ory of R ank T ests bo ok (H´ ajek and ˇ Sid´ ak, 1967 ). After muc h effort, the sec- ond, enlarged edition came out from Academic Press in 1999 (H´ ajek, ˇ Sid´ ak and Sen, 1999 ). Bac k in the 1980s I was in terested in constrained statistical in- ference, esp ecially in nonparametric setups. T w o year- long visits of Mervyn Silv apulle ultimately resulted in the 2004 b o ok on this broad area encompassing parametrics as w ell as b ey ond parametrics (Silv a- pulle and Sen, 2004 ). Ghosh: Let’s talk ab out y our famous b o ok with Madan Puri on multiv ariate rank tests published in 1971 (Puri and Sen, 1971 ). What w as the in tended audience for this b o ok? Sen: L ehmann’s 1959 hyp othesis testing b o ok (Lehmann, 1959 ) and the H´ ajek– ˇ Sid´ ak The ory of R ank T ests set the audience at the sta tistics gradu- ate lev el. Th is led us to consider a little less abstract treatise of the su b ject m atter, y et still aimed at the same lev el. W e u sed to share a jok e at that time: H´ ajek– ˇ Sid´ ak ( 1967 ) and Pu r i–Sen ( 1971 ) led Erich Lehmann to w r ite an ev en simpler nonparametrics b o ok in 1974. If I w ould hav e rewritten this 1971 text, it w ould hav e b een more in line with our 1997 sequen tial estimation lev el, emphasizing stati stical in terpretations more than asymptotics. Ghosh: Y ou co-edited tw o v olumes for the Hand- b o ok of Statistics and cont ribu ted numerous articles to the Encyclop e dia of Statistic al Sci e nc e (and Bio- statistic s). What impact d o you think that these publications h ad ? Sen: In the 1970s, I wa s caugh t in th e middle of abstract theoretical develo pments and the m uc h needed app licatio ns where the metho dology w ould b e very helpful. F aced with this dilemma, the t wo Handb o ok of Statistics vol umes, n onparametrics w ith P . R. Krishnaiah (Krishnaiah and Sen, 1984 ), and bio en vironmenta l and public health with C. R. Rao (Sen and Rao, 2000 ), were an effort to illustrate the role of statisti cal metho d ology in v arious interdisci- plinary fi elds of applications. The en cyclop edia arti- cles were of the nont ec hnical exp ository t yp e for the con v enience of users wh o lac k more complete statis- tical exp ertise; it has served w ell from a reference material p ersp ectiv e, and I am happy to see that suc h metho ds are getting more att enti on in recen t applied works. Ghosh: Y ou are an editor of Se quential Anal ysis . Can y ou commen t on the stature of that journ al? Sen: The thrust for sp ecializ ed journ als arose in the 197 0s, p artly fueled b y the shortage of space in the so ciet y journals (AMS, JASA) and partly to ac- commo d ate more in-depth presen tation of sp ecial- ized work. I w as on the found ing editorial b oard of the J ournal of Multivariate Analysis (19 72) and the Communic ations in Statistics , around the same time. My college friend Bhask ar Ghosh (at Leh igh) w as v ery muc h in the mainstream of sequen tial hy- p othesis testing, w riting a well-rec eiv ed b o ok around 1970, while time-sequen tial, rep eated significance testing, group sequent ial metho ds, and nonparamet- rics we re mostly deve lop ed later in that d ecade. So, in 1980 wh en Marcel Dekk er r equested that we start a new journal in this area , w e discussed the pro ject with a n umb er of activ e researc hers in this field. I am happy to s ay that w e receiv ed o ve rwh elming su pp ort and man y of them joined the edito rial b oard. After A CON V ERSA TION WITH PRANA B KUMAR SEN 15 15 yea rs, w e handed ov er the editorial r esp onsibili- ties to Mala y , who du tifully promoted the area for an additional 8 y ears. The presen t editorial b oard is muc h more div ersified with man y more members. I w onder whether this diversificat ion (presum ably in viting s ome dilution) is really ideal for su c h a sp e- cialize d area. Ho we ve r, b eing less inv olv ed for the past 5 y ears, I should r esist my temptation in pass- ing comments in an y w a y . Ghosh: Y ou were the third recipient of the presti- gious Senior No ether Aw ard, after Eric h Lehmann and Bob Hogg. Th is b ears a strong testimon y to y our man y contributions to n onparametric statis- tics. Do y ou d istinguish b et w een the classical and mo dern n onparametric statistics, suc h as sp line smo othing and density estimation, etc.? Sen: I was pleasan tly surprised in b eing aw ard ed, more so as Eric h and Bob were in their late sev en- ties or early eigh ties wh ereas I w as some 15 y ears y ounger. Ho wev er, I am happ y to see that, w ith th e exception of Manny P arzen (2005), the a wa rd ees af- ter m e were all in my age group. Lik e any other field, in nonp arametrics to o, the “quick and d irt y meth- o ds” (Mosteller, 1948 ), d uring the 1950 s to 1990 s, led to an ev olution of no vel methodology , encom- passing a m uc h wider area, including m ultiv ariate, sequen tial and general linear mo dels, along w ith ap - plications in dosimetry , bio equiv alence and clinical trials (surviv al analysis). In my ju d gmen t, a sig- nifican t ann exation to this arena is semiparamet- rics, spark ed in the 1970s by the s eminal wo rks of Da vid Co x ( 1972 ), and the CAR T methodology de- v elop ed in the W est Coast a few y ears later. Spline smo othing, density estimatio n and, more generally , nonparametric regression are v ery m uc h in the in- ner core of nonparametrics and still reside there. The other t w o dev elopment s are somewhat different. Their genesis is in nonp arametrics, and y et semi- parametrics d ominate their nurture. Ha vin g said that, I still regard them to b e w ithin the core of non- parametrics (which, by no means, is limited to rank statistic s or exact distribution-free metho ds ). Ho w- ev er, their dep endence on compu tationall y in tensiv e to ols often calls for data minin g or statistica l learn- ing tools. There app ears to b e an undercu r ren t for these areas to b r anc h out of n onparametrics int o separate sub disciplines. I w ould s imp ly prescrib e a single phrase— Beyond Par ametrics —to include all these ev olutions under a common umbrella. Sc hell: There are four statistic ians wh o ha v e co- authored at least 10 pap ers with you: Drs. S aleh, Mala y Ghosh, Madan Pu ri and Jana J ure ´ ck o v´ a. Please talk ab out these k ey collaborations. Sen: I p refer to judge the impact of collab oration not b y the num b er of co-authored pap ers but b y their qualit y . In this resp ect, the most imp ortan t one w as with Shoutir Chatterjee, whic h really laid down the foundation of m ultiv ariate nonp arametrics that w as follo wed thr ough by other subsequ ent collabora- tors. I am sure that if Chatterjee were in the USA, w e w ould ha ve had m an y more join t pub licatio ns, not only in multiv ariate nonparametrics but also in time-sequen tial metho d s where his impact h as b een tremendous. Madan Puri and I w ere b oth yo ung and full of energy in the late 196 0s and it has b een a v ery helpful exp erience for me to work with h im for ab out 15 y ears. The other significant imp act in the area of sequenti al nonparametrics (ev en going o v er to the Pitman clo seness and empir ical Ba y es meth- o ds) has b een due to Mala y . F rom Jana, I gained m uc h insight in to robu st metho ds. Dr. Saleh’s case is somewhat different. He had some ideas on pr elim- inary test estimators in the 1970s. I tol d him that the asymptotics that had b een r ecen tly devel op ed could b e successfully incorp orated in this area. W e follo wed thr ough on these ideas during the next 15 y ears or so, resulting in a num b er of pu blications. Ho w ev er, it b ecame clear to us th at such estimators w ere uniformly dominated by the Stein-t yp e shr ink- age estimators, as shown in my 1986 Sankhya p ap er (Sen, 1986 ). Thus, our w ork s hifted to hierarc hical and empirical Ba y es analog ues of p reliminary test estimators. Mala y , y ou ma y reca ll our join t p ap er with y ou in that arena also. I should also ment ion that Manish Bhatt ac harjee and Y ogendra Chaub ey hav e collab orated with m e on some in teresting ideas in reliabilit y theory and functional estima tion. Sc hell: T o date, yo u ha ve sup ervised 80 graduate studen ts. Man y of them ha v e b ecome successful in later y ears, either in academia or go v ernment. Ho w did you stimulate their en thusiasm for statist ics? Sen: A man is known by the compan y h e kee ps, and a professor’s compan y is his/her advisees and collea gues. On b oth coun ts, I am fortun ate. T he tra- dition of outstanding gradu ate studen ts in Statistics w as and is quite str ong. In 1969 I started also sup er- vising student s in Biostatistics; many of them ha v e go o d metho dological bac kground but we re application-o riente d. I am happy that in such cases, I co uld direct them in the right p ersp ectiv es, albeit 16 M. GHO SH AND M. J. SCHELL they excelled on their o wn merits. It was statisti - cally exp ected that s ome very brigh t stud en ts we re in greater n eed for more advising for concen tration and lo caliz ation of dissertation work. It wa s my plea- sure to see that most of them made it with honor and dignit y . REFLECTIONS ON ST A TISTICS, NONP ARAMETRICS AND RELIGION Sc hell: What is y our assessmen t ab out the futur e of statistics and biostatistics? Where do yo u th in k that w e are heading? Sen: I wish I could m utter: Que Sera, Sera. What- ev er will b e, will b e. The future’s n ot ours to (fore)see. Eac h discipline is going through ev olutionary c hanges, and ours is no exception. Application-o riente d and dominated researc h is reshaping basic researc h in sciences, while the computer and information tec h- nology is totally engulfing th e p ersp ectiv es of the exp eriment al sciences. Statistica l science, including statistic s and biostatistics, has its genesis in mathe- matics bu t has ev olv ed into in terdisciplinary fields. Medical studies, clinica l trials, en vironmen tal health sciences, reliabilit y studies, and genomics and bioin- formatics are kno cki ng at the do ors . It’s a basic task to establish the statisti cal basis in such exp erimen tal fields and dev elop metho dological researc h to suit the pu r p ose w ell. Data minin g and other compu ta- tional algorithms are w orking out well , and y et there is a p rofound n eed for implemen tation of v alid, r o- bust and efficient statistic al reasoning in suc h app li- cations. Mathematical abstractions in statistics are fading a w a y , giving w ay to graphical disp lays and magical n umerical outp u ts from the sup ercomput- ers. Alas, I wish I could attac h some v alidatory sta- tistical in terpretations to them. The Ba yesian meth- o ds are promising, alb eit they need to b e tun ed with prop er priors, not the v ague ones. Ha ving said so, I am also v ery hop eful that smart metho dological re- searc hers in statistics will find a wa y out to salv age their method ologic al w orks b efore unconditionally submitting to the wind p ip es of data mining. Sc hell: Do yo u think that nonparametric metho d s are appreciated sufficien tly by the statistic s comm u- nit y tod a y? Sen: Is there an y wa y not to do that? Th e limi- tations of the classical parametrics are b ecoming so eviden t that either the c hoice is to surr ender to data mining or to go “b ey ond parametrics.” On a p ositiv e side, nonp arametrics ha v e a natur al app eal r egard- ing their scop e of applicabilit y and mo d el flexibilit y . On the n egativ e side, they ma y inh erit larger sam- ple size requiremen ts in order to h a v e adequate pr e- cision of drawn stati stical conclusions. F ortunately , with the adv ent of mo dern computers, large data sets n o w dominate statistical mod eling and analy- sis, and hence, nonparametrics are b eing receiv ed increasingly b y th e statistics comm u nit y . Of course, I m ust wa rn that use of data min ing tools ma y not automatica lly qualify for inclusion in this p r escrip- tion, and hence, that needs to b e app r aised prop erly . Ghosh: On e of y our fa v orite pastimes is stud ying b o oks on religion, especially those written on Ra- makrishna, Vive k ananda or Saradamani. Y ou also write p o etry in b oth En glish and Bengali. Do y ou w an t to commen t on that? Sen: I confess that I d o not qualify for tennis or con tract b ridge nor ha v e any talent for piano or violin. Moreo ve r, dur in g my school d a ys, I had little app etite for literature or newspap er reading. My mother u sed to w orry ab out my prosp ects. Just three months after the matriculation examination, I sta rted r eading classical no v els of con temp orary Bengali wr iters, bu t did not get muc h out of it. In the midst of that, my reading the “Sancha yita” of Rabindra Nath T agore completely c hanged m y views. The more I read the more I was fascinated b y the lyrical p o w ers of this great p o et of all times. The collecti on on “Puj a” and “Prakriti” were the cream of his u nderstanding of the nature and the lord in a broad sense. Y ears later, I lo oke d first into the writings of Swa mi Viv ek anada which to ok me to another world. In due course I also read the “Gosp el of Ramakrishna” with deep curiosit y . I started won- dering how they realized Go d in their o wn wa y , and y et how parallel were their lines of thinking. I am re- ligious bu t am neither an ortho do x nor a fun d amen- talist. My feeling is almost the w a y T agore d epicted in his “Geetanjali” : Offer thy he art, mind and soul at the fe et of the almighty, without any exp e c tation; Suddenly you would r e alize how insignifi- c ant we ar e in this time and sc ale of p er- c eption. T agore’s approac h w as a lyrica l one whic h sup- presses all pains of b o dy and mind and enables one to concen trate in appreciating the sup erp erson in our life-cycle. The origin of p o etry lies in the same appreciation. Man y things that yo u cannot express in plain p rose can b e comp osed su ccinctly in a verse, con v eying the deep er m eaning whic h r eac hes the A CON V ERSA TION WITH PRANA B KUMAR SEN 17 heart easily . T o me this is the ideal wa y of r ealiza- tion of w hatev er I ma y aspire. My comp osition of little p o ems in b oth Bengali and English is far from b eing p erfect or on par with con temp orary w orks by others. Y et that giv es me a sense of esteem that I lo v e to hav e. I hop e to b e able to dip in to this in the near f uture. Ghosh: I u nderstand that yo u are planning to re- tire officially in a few years. If I kno w y ou, y ou are nev er going to giv e up statistic s. But do y ou hav e an y other plans after retiremen t? Sen: I wo uld like to tak e off fr om in -class teac hin g and sup ervision of do ctoral student s, culminating in an officia l reti rement in th e near future. How ever, that should not put a roadblo c k to my p ursuit of statistic al reasoning in a greater domain. I am fasci- nated by the cur ren t d ev elopmen t of bioinformatics and environmetrics; there is a tremendous scop e for statistic al reasoning in such cont exts. Qualit y of life is another area that att racts me more at this stage. The religious inclinations I ha ve should help me in appraising this asp ect in a br oader s p ectrum. But, ha ving said so, I must also say that r etirement is a natural phase and I should accept it in a natural w a y mingled with the presen t state of my m ind. Ghosh: Is there anyt hing else that y ou wish to talk ab out that we failed to ask y ou? Sen: Mala y and Mic hael, I am indeed v ery happ y that y ou ha v e undertak en th is con v ersation with me. I w ould lik e to express my thanks to the UNC Sc ho ol of Public Health Dean Pr ofessor Barbara Rimer and Ms. Martha Monnett for their in terest and arranging this con v ersation taking place at the Sp eec h Com- m unication Cen ter, UNC. Let m e tak e this opp ortunit y to exp r ess my ap- preciation for all m y colleag ues and others in a few lines (adapted from T agore): Who ever imp arte d splashes of happiness in my life, I b ow to you, and who ever in- flicte d sufferings in my he art, I b ow to you to o. Al l wh o have lighte d th e c and le of love in my life, showing the way to ap- pr e ciate everyone, I b ow to you to o. What- ever c ame in my wa y, touche d my he art, or gone far away, alb eit, in a distant p ath, I b ow to you al l in the same way. Know- ingly or not, admitte d ly or not, I have r e- alize d Thou: O h, H oly Mother, and b owing in pr ostr ation, I long for you. Statistics is indisp ensable in ev ery walk of life and sci- enc e; at this b end of the walk, let hop e and faith guide my c onscienc e. REFERENCES Adichie, J. N. (1967). Estimation of regression parame- ters based on rank t ests. A nn. Math. Stat ist . 38 894–904. MR024771 5 Balakrishnan, N., Pena, E. and Sil v apulle, M. J. 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