Improved robust model selection methods for the Levy nonparametric regression in continuous time

TL;DR

This paper introduces an improved model selection method for Levy nonparametric regression in continuous time, enhancing accuracy and robustness through adaptive procedures and oracle inequalities.

Contribution

It develops a James-Stein type estimator and an adaptive model selection procedure with proven efficiency and sharp oracle inequalities for Levy-driven nonparametric regression.

Findings

Significant accuracy improvement in nonparametric models

Establishment of sharp oracle inequalities

Demonstration of efficiency in adaptive model selection

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.