Improved model selection method for an adaptive estimation in semimartingale regression models. (English) Zbl 1497.62100
Summary: This paper considers the problem of robust adaptive efficient estimating of a periodic function in a continuous time regression model with the dependent noises given by a general square integrable semimartingale with a conditionally Gaussian distribution. An example of such noise is the non-Gaussian Ornstein-Uhlenbeck-Lévy processes. An adaptive model selection procedure, based on the improved weighted least square estimates, is proposed. Under some conditions on the noise distribution, sharp oracle inequality for the robust risk has been proved and the robust efficiency of the model selection procedure has been established. The numerical analysis results are given.
MSC:
| 62G08 | Nonparametric regression and quantile regression |
| 62G05 | Nonparametric estimation |
| 62G20 | Asymptotic properties of nonparametric inference |
Keywords:
improved non-asymptotic estimation; least squares estimates; robust quadratic risk; nonparametric regression; semimartingale noise; Ornstein-Uhlenbeck-Lévy process; model selection; sharp oracle inequality; asymptotic efficiencyReferences:
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