Partial heteroscedastic deconvolution estimation in nonparametric regression

TL;DR

This paper introduces a kernel-based partial deconvolution estimator for nonparametric regression with heteroscedastic measurement errors, achieving optimal convergence rates and demonstrating good finite-sample performance.

Contribution

It proposes a novel kernel estimator for regression with mixed error measurement, extending existing methods to heteroscedastic error settings.

Findings

Achieves optimal convergence rate under regularity conditions.

Performs well in finite-sample simulations.

Addresses heteroscedastic measurement errors in regression estimation.

Abstract

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.