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 journalArticle

1 Citation (Scopus)

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 languageEnglish
Pages (from-to)73-77
Number of pages5
JournalCommunications - Scientific Letters of the University of Zilina
Volume20
Issue number1
Publication statusPublished - 1 Jan 2018

Fingerprint

selection procedure
time
Model selection
Weighted least squares
Continuous time
Nonparametric estimation

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

  • Automotive Engineering
  • Transportation
  • Economics and Econometrics
  • Computer Networks and Communications

Cite this

@article{f4a7125026534dc886072f6929c0a9e8,
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 = "1",
day = "1",
language = "English",
volume = "20",
pages = "73--77",
journal = "Communications - Scientific Letters of the University of Zilina",
issn = "1335-4205",
publisher = "University of Zilina",
number = "1",

}

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

UR - http://www.scopus.com/inward/record.url?scp=85044251794&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85044251794&partnerID=8YFLogxK

M3 - Article

VL - 20

SP - 73

EP - 77

JO - Communications - Scientific Letters of the University of Zilina

JF - Communications - Scientific Letters of the University of Zilina

SN - 1335-4205

IS - 1

ER -