Asymptotically efficient estimators for nonparametric heteroscedastic regression models

TL;DR

This paper develops asymptotically efficient kernel estimators for nonparametric heteroscedastic regression models, achieving minimax absolute error risk in both Gaussian and unknown noise distribution cases.

Contribution

It introduces a novel kernel estimator that is asymptotically optimal for heteroscedastic models with different noise distributions.

Findings

Estimator is asymptotically efficient under Gaussian noise.

Estimator achieves minimax absolute error risk.

Applicable to models with unknown noise distribution.

Abstract

This paper concerns the estimation of the regression function at a given point in nonparametric heteroscedastic models with Gaussian noise or with noise having unknown distribution. In the two cases an asymptotically efficient kernel estimator is constructed for the minimax absolute error risk.