Improved robust model selection methods for a Lévy nonparametric regression in continuous time. Issue 3 (3rd July 2019)

• Record Type: Journal Article
• Authors: Pchelintsev, E. A.; Pchelintsev, V. A.; Pergamenshchikov, S. M.
• Is Part Of: Journal of nonparametric statistics. Volume 31:Issue 3(2019)
• Page Start: 612
• Page End: 628
• Publication Date: 2019-07-03
• Subjects: Improved non-asymptotic estimation -- James–Stein procedures -- robust quadratic risk -- nonparametric regression -- Lévy process -- model selection -- sharp oracle inequality -- adaptive estimation -- asymptotic efficiency; 62G08 -- 62G05; Nonparametric statistics -- Periodicals; 519.5
• DOI: 10.1080/10485252.2019.1609672
• Languages: English
• ISSNs: 1048-5252

Abstract

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.