Work

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

Year: 2019

Type: article

Abstract: 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.

Source: Journal of nonparametric statistics

DOI: 10.1080/10485252.2019.1609672

Authors: E. A. Pchelintsev, V. A. Pchelintsev, S. M. Pergamenshchikov

Institutions: National Research Tomsk State University, Tomsk Polytechnic University, Laboratoire de Mathématiques Raphaël Salem, Université de Rouen Normandie

Language: English

Topic: Statistical Methods and Inference

Subfield: Statistics and Probability

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: Ministerstwo Edukacji i Nauki, Russian Science Foundation

Award: G4050893089