Improved robust model selection methods for the Levy nonparametric regression in continuous time
Statistics Theory
2019-09-17 v2 Statistics Theory
Abstract
In this paper we develop the James - Stein improved estimation method for a nonparametric periodic function observed with the Levy noises in continuous time. An adaptive model selection procedure based on the improved weighted least square estimates is constructed. The improvement effect for the nonparametric models is obtained. It turns out that in the nonasymptotic studies the accuracy improvement for nonparametric problems is more significantly than for the parametric one. Moreover, sharp oracle inequalities for the robust risks have been shown and the efficiency property for the improved model selection procedure has been established in the adaptive setting.
Cite
@article{arxiv.1710.03111,
title = {Improved robust model selection methods for the Levy nonparametric regression in continuous time},
author = {Evgeny Pchelintsev and Valerii Pchelintsev and Serguei Pergamenshchikov},
journal= {arXiv preprint arXiv:1710.03111},
year = {2019}
}
Comments
arXiv admin note: text overlap with arXiv:1611.07378