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
N1 - Funding Information:
The results of section 2 of this work are supported by the Ministry of Education and Science of the Russian Federation in the framework of the research project no. 2.3208.2017/4.6 and the RFBR Grant 16-01-00121 A. The results of Section 3 are supported by the RSF grant number 14-49-00079 (National Research University “MPEI”, Moscow, Russia). The last author is partially supported by the Russian Federal Professor program (project no. 1.472.2016/1.4, Ministry of Education and Science) and by the project XterM-Feder, University of Rouen.
Funding Information:
The results of section 2 of this work are supported by the Ministry of Education and Science of the Russian Federation in the framework of the research project no. 2.3208.2017/4.6 and the RFBR Grant 16-01-00121 A. The results of Section 3 are supported by the RSF grant number 14-49-00079 (National Research University "MPEI", Moscow, Russia). The last author is partially supported by the Russian Federal Professor program (project no. 1.472.2016/1.4, Ministry of Education and Science) and by the project XterM-Feder, University of Rouen.
Publisher Copyright:
© 2018 University of Zilina. All rights reserved.
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
M3 - Article
AN - SCOPUS:85044251794
SN - 1335-4205
VL - 20
SP - 73
EP - 77
JO - Communications - Scientific Letters of the University of Zilina
JF - Communications - Scientific Letters of the University of Zilina
IS - 1
ER -