Non asymptotic sharp oracle inequalities for the improved model selection procedures for the adaptive nonparametric signal estimation problem

Evgeny Pchelintsev; Valeriy Pchelintsev; Serguei Pergamenshchikov

Non asymptotic sharp oracle inequalities for the improved model selection procedures for the adaptive nonparametric signal estimation problem

Evgeny Pchelintsev, Valeriy Pchelintsev, Serguei Pergamenshchikov

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

8 Scopus citations

Abstract

In this paper, we consider the robust adaptive non parametric estimation problem for the periodic function observed with the Levy noises in continuous time. An adaptive model selection procedure, based on the improved weighted least square estimates, is proposed. Sharp oracle inequalities for the robust risks have been obtained.

Original language	English
Pages (from-to)	73-77
Number of pages	5
Journal	Communications - Scientific Letters of the University of Zilina
Volume	20
Issue number	1
State	Published - 1 Jan 2018
Externally published	Yes

Keywords

Asymptotic efficiency
Improved non-asymptotic estimation
Levy process
Model selection
Non-parametric regression
Robust quadratic risk
Sharp oracle inequality
Weighted least squares estimates

ASJC Scopus subject areas

Civil and Structural Engineering
Transportation
Mechanical Engineering
Electrical and Electronic Engineering

Cite this

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title = "Non asymptotic sharp oracle inequalities for the improved model selection procedures for the adaptive nonparametric signal estimation problem",

abstract = "In this paper, we consider the robust adaptive non parametric estimation problem for the periodic function observed with the Levy noises in continuous time. An adaptive model selection procedure, based on the improved weighted least square estimates, is proposed. Sharp oracle inequalities for the robust risks have been obtained.",

keywords = "Asymptotic efficiency, Improved non-asymptotic estimation, Levy process, Model selection, Non-parametric regression, Robust quadratic risk, Sharp oracle inequality, Weighted least squares estimates",

author = "Evgeny Pchelintsev and Valeriy Pchelintsev and Serguei Pergamenshchikov",

year = "2018",

month = jan,

day = "1",

language = "English",

volume = "20",

pages = "73--77",

journal = "Communications - Scientific Letters of the University of Zilina",

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publisher = "University of Zilina",

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Non asymptotic sharp oracle inequalities for the improved model selection procedures for the adaptive nonparametric signal estimation problem. / Pchelintsev, Evgeny; Pchelintsev, Valeriy; Pergamenshchikov, Serguei.
In: Communications - Scientific Letters of the University of Zilina, Vol. 20, No. 1, 01.01.2018, p. 73-77.

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

TY - JOUR

T1 - Non asymptotic sharp oracle inequalities for the improved model selection procedures for the adaptive nonparametric signal estimation problem

AU - Pchelintsev, Evgeny

AU - Pchelintsev, Valeriy

AU - Pergamenshchikov, Serguei

PY - 2018/1/1

Y1 - 2018/1/1

N2 - In this paper, we consider the robust adaptive non parametric estimation problem for the periodic function observed with the Levy noises in continuous time. An adaptive model selection procedure, based on the improved weighted least square estimates, is proposed. Sharp oracle inequalities for the robust risks have been obtained.

AB - In this paper, we consider the robust adaptive non parametric estimation problem for the periodic function observed with the Levy noises in continuous time. An adaptive model selection procedure, based on the improved weighted least square estimates, is proposed. Sharp oracle inequalities for the robust risks have been obtained.

KW - Asymptotic efficiency

KW - Improved non-asymptotic estimation

KW - Levy process

KW - Model selection

KW - Non-parametric regression

KW - Robust quadratic risk

KW - Sharp oracle inequality

KW - Weighted least squares estimates

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M3 - Article

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SN - 1335-4205

VL - 20

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JO - Communications - Scientific Letters of the University of Zilina

JF - Communications - Scientific Letters of the University of Zilina

IS - 1

ER -

Non asymptotic sharp oracle inequalities for the improved model selection procedures for the adaptive nonparametric signal estimation problem

Abstract

Keywords

ASJC Scopus subject areas

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