Robust adaptive efficient estimation for semi-Markov nonparametric regression models

Vlad Stefan Barbu (), Slim Beltaief () and Sergey Pergamenshchikov ()
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Vlad Stefan Barbu: UMR 6085 CNRS-Université de Rouen
Slim Beltaief: UMR 6085 CNRS-Université de Rouen
Sergey Pergamenshchikov: UMR 6085 CNRS-Université de Rouen

Statistical Inference for Stochastic Processes, 2019, vol. 22, issue 2, No 2, 187-231

Abstract: Abstract We consider the nonparametric robust estimation problem for regression models in continuous time with semi-Markov noises. An adaptive model selection procedure is proposed. Under general moment conditions on the noise distribution a sharp non-asymptotic oracle inequality for the robust risks is obtained and the robust efficiency is shown. It turns out that for semi-Markov models the robust minimax convergence rate may be faster or slower than the classical one.

Keywords: Non-asymptotic estimation; Robust risk; Model selection; Sharp oracle inequality; Asymptotic efficiency; Primary 62G08; Secondary 62G05 (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s11203-018-9186-8

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