Improved robust model selection methods for a Lévy nonparametric regression in continuous time

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Improved robust model selection methods for a Lévy nonparametric regression in continuous time	1 MB	Adobe Acrobat PDF	Read	Download
DOI Доступ к ресурсу на сайте издателя			10.1080/10485252.2019.1609672

Title: Improved robust model selection methods for a Lévy nonparametric regression in continuous time
Creator: Pchelintsev, Evgeny A.
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Pchelintsev, Valeriy A.
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Pergamenshchikov, Serguei M.
Date: 2019
DOI: 10.1080/10485252.2019.1609672
Description: In this paper, we develop the James–Stein improved method for the estimation problem of a nonparametric periodic function observed with Lévy noises in continuous time. An adaptive model selection procedure based on the weighted improved least squares estimates is constructed. The improvement effect for nonparametric models is studied. It turns out that in non-asymptotic setting the accuracy improvement for nonparametric models is more important than for parametric ones. Moreover, sharp oracle inequalities for the robust risks have been shown and the adaptive efficiency property for the proposed procedures has been established. The numerical simulations are given.