Journal article

Nonparametric regression estimation in the heteroscedastic errors-in-variables problem

Aurore Delaigle, Alexander Meister

JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION | AMER STATISTICAL ASSOC | Published : 2007

Abstract

In the classical errors-in-variables problem, the goal is to estimate a regression curve from data in which the explanatory variable is measured with error. In this context, nonparametric methods have been proposed that rely on the assumption that the measurement errors are identically distributed. Although there are many situations in which this assumption is too restrictive, nonparametric estimators in the more realistic setting of heteroscedastic errors have not been studied in the literature. We propose an estimator of the regression function in such a setting and show that it is optimal. We give estimators in cases in which the error distributions are unknown and replicated observations..

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University of Melbourne Researchers