This article is cited in 7 papers

MATHEMATICS

Non-parametric estimation in a semimartingale regression model. Part 1. Oracle inequalities

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

a</sup> Tomsk State Uneversity, Department of Applied Mathematics
^b Tomsk State University, Faculty of Mechanics and Mathematics
^c Laboratoire de Mathematiques Raphael Salem

Abstract: This paper considers the problem of estimating a periodic function in a continuous time regression model with a general square integrable semimartingale noise. A model selection adaptive procedure is proposed. Sharp non-asymptotic oracle inequalities have been derived.

Keywords: Non-asymptotic estimation; Non-parametric regression; Model selection; Sharp oracle inequality; Semimartingale noise.

UDC: 519.2


Accepted: August 26, 2009