Oracle inequalities for the stochastic differential equations E. A. Pchelintsev, S. M. Pergamenshchikov
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ArticleContent type: Текст Media type: электронный Subject(s): непараметрическая регрессия | взвешенные оценки наименьших квадратов | улучшенные неасимптотические оценки | Леви процесс | Орнштейна-Уленбека процесс | полумарковские процессы | выбор модели | неравенство оракула | асимптотическая эффективность | адаптивная оценкаGenre/Form: статьи в журналах Online resources: Click here to access online
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Statistical inference for stochastic processes Vol. 21, № 2. P. 469-483Abstract: 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.
Библиогр.: с. 482-483
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.
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