This article is cited in 4 papers

MATHEMATICS

Improved model selection method for an adaptive estimation in semimartingale regression models

E. A. Pchelintsev^a, S. M. Pergamenshchikov<sup>b

a</sup> Department of Mathematics and Mechanics, National Research Tomsk State University, Tomsk, Russia
^b Laboratory of Mathematics Raphael Salem, University of Rouen Normandy, France

Abstract: This paper considers the problem of robust adaptive efficient estimating of a periodic function in a continuous time regression model with the dependent noises given by a general square integrable semimartingale with a conditionally Gaussian distribution. An example of such noise is the non-Gaussian Ornstein–Uhlenbeck–Levy processes. An adaptive model selection procedure, based on the improved weighted least square estimates, is proposed. Under some conditions on the noise distribution, sharp oracle inequality for the robust risk has been proved and the robust efficiency of the model selection procedure has been established. The numerical analysis results are given.

Keywords: improved non-asymptotic estimation, least squares estimates, robust quadratic risk, non-parametric regression, semimartingale noise, Ornstein–Uhlenbeck–Levy process, model selection, sharp oracle inequality, asymptotic efficiency.

UDC: 519.2

MSC: 62G08; 62G05

Received: 13.11.2018

Language: English

DOI: 10.17223/19988621/58/2

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