language: en

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

Konev, V. ? S. Pergamenshchikov ?
September 16, 2009

Abstract In this paper we prove the asymptotic efficiency of the model selection procedure proposed by the authors in [10]. 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. AMS 2000 Subject Classifications: Primary: 62G08; Secondary: 62G05

[* The paper is supported by the RFFI-Grant 09-01-00172-a.]

? Department of Applied Mathematics and Cybernetics, Tomsk State University,
Lenin str. 36, 634050 Tomsk, Russia,
e-mail: vvkonev@mail.tsu.ru
? Laboratoire de Mathématiques Raphael Salem,
Avenue de l'Université, BP. 12,
Université de Rouen,
F76801, Saint Etienne du Rouvray, Cedex France,
Department of Mathematics and Mechanics,Tomsk State University,
Lenin str. 36, 634041 Tomsk, Russia,
e-mail: Serge.Pergamenchtchikov@univ-rouen.fr

[1]

hal-00417600, version 1 - 16 Sep 2009

1 Introduction