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Vestnik Tomskogo Gosudarstvennogo Universiteta. Matematika i Mekhanika, 2019, Number 58, Pages 14–31
DOI: https://doi.org/10.17223/19988621/58/2
(Mi vtgu696)
 

This article is cited in 3 scientific papers (total in 3 papers)

MATHEMATICS

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

E. A. Pchelintseva, S. M. Pergamenshchikovb

a Department of Mathematics and Mechanics, National Research Tomsk State University, Tomsk, Russia
b Laboratory of Mathematics Raphael Salem, University of Rouen Normandy, France
Full-text PDF (529 kB) Citations (3)
References:
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.
Funding agency Grant number
Russian Science Foundation 17-11-01049
Ministry of Education and Science of the Russian Federation 2.3208.2017/4.6
1.472.2016/1.4
This work is supported by RSF, Grant no 17-11-01049.
Received: 13.11.2018
Bibliographic databases:
Document Type: Article
UDC: 519.2
MSC: 62G08; 62G05
Language: English
Citation: E. A. Pchelintsev, S. M. Pergamenshchikov, “Improved model selection method for an adaptive estimation in semimartingale regression models”, Vestn. Tomsk. Gos. Univ. Mat. Mekh., 2019, no. 58, 14–31
Citation in format AMSBIB
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\by E.~A.~Pchelintsev, S.~M.~Pergamenshchikov
\paper Improved model selection method for an adaptive estimation in semimartingale regression models
\jour Vestn. Tomsk. Gos. Univ. Mat. Mekh.
\yr 2019
\issue 58
\pages 14--31
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\crossref{https://doi.org/10.17223/19988621/58/2}
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  • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Вестник Томского государственного университета. Математика и механика
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    References:25
     
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