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

2008/04/10 by Leonid Galtchouk, Galtchouk, Leonid, Serguey Pergamenshchikov +1
Decision Sciences · Engineering · Mathematics · #Advanced Control Systems Optimization #FOS: Mathematics #Grey System Theory Applications #Iron and Steelmaking Processes #Statistics Theory (math.ST) #math.ST #stat.TH

paper · pdf · doi:10.48550/arxiv.0804.1584

arxiv created 2008/04/10 · openalex publication_date 2008/04/10 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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