Oracle inequalities for the stochastic differential equations

E. A. Pchelintsev () and S. M. Pergamenshchikov ()
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E. A. Pchelintsev: Tomsk State University
S. M. Pergamenshchikov: University of Rouen

Statistical Inference for Stochastic Processes, 2018, vol. 21, issue 2, No 13, 469-483

Abstract: Abstract This paper is a survey of recent results on the adaptive robust non parametric methods for the continuous time regression model with the semi-martingale noises with jumps. The noises are modeled by the Lévy processes, the Ornstein–Uhlenbeck processes and semi-Markov processes. We represent the general model selection method and the sharp oracle inequalities methods which provide the robust efficient estimation in the adaptive setting. Moreover, we present the recent results on the improved model selection methods for the nonparametric estimation problems.

Keywords: Non-parametric regression; Weighted least squares estimates; Improved non-asymptotic estimation; Robust quadratic risk; Lévy process; Ornstein–Uhlenbeck process; Semi-Markov process; Model selection; Sharp oracle inequality; Adaptive estimation; Asymptotic efficiency; Primary 62G08; Secondary 62G05 (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s11203-018-9180-1

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