Improved robust model selection methods for a Lévy nonparametric regression in continuous time /E. A. Pchelintsev, V. A. Pchelintsev, S. M. Pergamenshchikov

Pchelintsev, Evgeny A.
Электронный ресурс
Другой Автор
Pchelintsev, Valeriy A.
Pergamenshchikov, Serguei M.
Источник
Journal of nonparametric statistics 2019 Vol. 31, № 3. P. 612-628
Аннотация
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.
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Резюме
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.