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Improved model selection method for an adaptive estimation in semimartingale regression models E. A. Pchelintsev, S. M. Pergamenshchikov

By: Pchelintsev, Evgeny AContributor(s): Pergamenshchikov, Serguei MMaterial type: ArticleArticleOther title: Улучшенный метод выбора модели для адаптивного оценивания в семимартингальных регрессионных моделях [Parallel title]Subject(s): улучшенное неасимптотическое оценивание | оценки наименьших квадратов | робастный квадратический риск | непараметрическая регрессия | семимартингальный шум | выбор модели | точное оракульное неравенство | асимптотическая эффективность | Орнштейна-Уленбека-Леви процессGenre/Form: статьи в журналах Online resources: Click here to access online In: Вестник Томского государственного университета. Математика и механика № 58. С. 14-31Abstract: 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.
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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.

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