Optimal confidence intervals for bounded parameters (a correct alternative to the recipe of Feldman and Cousins)

A priori bound for the parameter to be estimated is incorporated into confidence intervals within frequentistic approach in a straightforward and optimal fashion, ensuring the best resolution of non-boundary values as well as robustness for non-physical values of the estimator.

💡 Research Summary

The paper addresses a long‑standing problem in frequentist interval construction: how to incorporate a priori bounds on a parameter (e.g., non‑negativity, an upper physical limit) without sacrificing coverage accuracy or producing overly conservative intervals. While the Feldman‑Cousins (F‑C) method introduced an ordering principle that respects such bounds, it often yields excessive over‑coverage near the boundary and can generate intervals that are unnecessarily wide when the estimator falls into an unphysical region. The authors propose a new “bounded‑parameter likelihood‑ratio ordering” that modifies the classic likelihood‑ratio ordering to explicitly account for the boundary constraints.

The method begins by partitioning the full parameter space Θ into a bounded region Θ_B =