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

E. A. Pchelintsev; V. A. Pchelintsev; S. M. Pergamenshchikov

doi:10.1080/10485252.2019.1609672

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

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

Research output: Contribution to journal › Article › peer-review

6 Scopus citations

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.

Original language	English
Pages (from-to)	612-628
Number of pages	17
Journal	Journal of Nonparametric Statistics
Volume	31
Issue number	3
DOIs	https://doi.org/10.1080/10485252.2019.1609672
State	Published - 3 Jul 2019
Externally published	Yes

Keywords

62G05
62G08
Improved non-asymptotic estimation
James–Stein procedures
Lévy process
adaptive estimation
asymptotic efficiency
model selection
nonparametric regression
robust quadratic risk
sharp oracle inequality

ASJC Scopus subject areas

Statistics and Probability
Statistics, Probability and Uncertainty

UN SDGs

This output contributes to the following UN Sustainable Development Goals (SDGs)

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10.1080/10485252.2019.1609672

Cite this

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title = "Improved robust model selection methods for a L{\'e}vy nonparametric regression in continuous time",

abstract = "In this paper, we develop the James–Stein improved method for the estimation problem of a nonparametric periodic function observed with L{\'e}vy 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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AU - Pchelintsev, E. A.

AU - Pchelintsev, V. A.

AU - Pergamenshchikov, S. M.

PY - 2019/7/3

Y1 - 2019/7/3

N2 - 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.

AB - 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.

KW - 62G05

KW - 62G08

KW - Improved non-asymptotic estimation

KW - James–Stein procedures

KW - Lévy process

KW - adaptive estimation

KW - asymptotic efficiency

KW - model selection

KW - nonparametric regression

KW - robust quadratic risk

KW - sharp oracle inequality

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DO - 10.1080/10485252.2019.1609672

M3 - Article

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VL - 31

SP - 612

EP - 628

JO - Journal of Nonparametric Statistics

JF - Journal of Nonparametric Statistics

IS - 3

ER -

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

Abstract

Keywords

ASJC Scopus subject areas

UN SDGs

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