Adaptive nonparametric estimation in heteroscedastic regression models. Part 2: Asymptotic efficiency

TL;DR

This paper proves that an adaptive nonparametric regression estimation method is asymptotically efficient, achieving the lowest possible quadratic risk in heteroscedastic models, extending previous work on its properties.

Contribution

It establishes the asymptotic efficiency of an adaptive estimation procedure in heteroscedastic nonparametric regression models.

Findings

The procedure attains the sharp lower bound for quadratic risk.

Asymptotic properties are rigorously proven.

The method is optimal in the sense of asymptotic quadratic risk.

Abstract

The paper deals with asymptotic properties of the adaptive procedure proposed in the author paper (2007) for estimation of unknown nonparametric regression. We prove that this procedure is asymptotically efficient for a quadratic risk. It means that the asymptotic quadratic risk for this procedure coincides with a sharp lower bound.