Spectral properties of the Neumann-Laplace operatorin quasiconformal regular domains
| Parent link: | Contemporary Mathematics Vol. 734 : Differential Equations, Mathematical Physics, and Applications: Selim Grigorievich Krein Centennial.— 2019.— [P. 129-144] |
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| Otros Autores: | , |
| Sumario: | Title screen 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. |
| Lenguaje: | inglés |
| Publicado: |
2019
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| Acceso en línea: | http://www.ams.org/books/conm/734/14768/conm734-14768.pdf |
| Formato: | Electrónico Capítulo de libro |
| KOHA link: | https://koha.lib.tpu.ru/cgi-bin/koha/opac-detail.pl?biblionumber=664240 |
| Sumario: | Title screen 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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