This article is cited in 6 papers

MATHEMATICS

Nonparametric estimation in a semimartingale regression model. Part 2. Robust asymptotic efficiency

V. V. Konev^a, S. M. Pergamenshchikov<sup>bc

a</sup> Tomsk State University
^b Université de Rouen
^c Tomsk State University, Faculty of Mechanics and Mathematics

Abstract: In this paper we prove the asymptotic efficiency of the model selection procedure proposed by the authors in [1]. To this end we introduce the robust risk as the least upper bound of the quadratical risk over a broad class of observation distributions. Asymptotic upper and lower bounds for the robust risk have been derived. The asymptotic efficiency of the procedure is proved. The Pinsker constant is found.

Keywords: Non-parametric regression; Model selection; Sharp oracle inequality; Robust risk; Asymptotic efficiency; Pinsker constant; Semimartingale noise.

UDC: 519.2

MSC: Primary 62G08; Secondary 62G05


Accepted: November 16, 2009

Language: English