Adaptive nonparametric estimation in heteroscedastic regression models. Part 1: Sharp non-asymptotic Oracle inequalities

TL;DR

This paper develops an adaptive nonparametric estimation method for heteroscedastic regression models with unknown variance, providing sharp non-asymptotic oracle inequalities for the quadratic risk.

Contribution

It introduces a new adaptive estimation procedure with non-asymptotic risk bounds for heteroscedastic regression, advancing the theoretical understanding of such models.

Findings

Established a non-asymptotic upper bound for quadratic risk.

Proved sharp oracle inequalities for the estimation procedure.

Demonstrated effectiveness in heteroscedastic regression settings.

Abstract

An adaptive nonparametric estimation procedure is constructed for the estimation problem of heteroscedastic regression when the noise variance depends on the unknown regression. A non-asymptotic upper bound for a quadratic risk (an oracle inequality) is constructed.