Partial heteroscedastic deconvolution estimation in nonparametric regression

In this paper, we consider a partial deconvolution kernel estimator for nonparametric regression when some covariates are measured with error while others are observed without error. We focus on a general and realistic setting in which the measurement errors are heteroscedastic. We propose a kernel-based estimator of the regression function in this framework and show that it achieves the optimal convergence rate under suitable regularity conditions. The finite-sample performance of the proposed estimator is illustrated through simulation studies.

💡 Research Summary

This paper addresses the problem of non‑parametric regression when the covariate vector consists of two parts: a set of variables that are observed without error and another set that is contaminated by measurement error. While the literature on errors‑in‑variables has largely focused on the case where all covariates are measured with error and the errors are homoscedastic (i.e., share a common distribution), the authors consider a more realistic scenario in which the measurement errors are heteroscedastic: each observation may have its own error distribution, possibly changing with the sample size.

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