Adaptive robust efficient estimation methods in statistical models generated by fractal Poisson processes S. Beltaief, V. S. Barbu, S. M. Pergamenshchikov
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ArticleContent type: Текст Media type: электронный Other title: Адаптивные робастные эф фективные методы оценивания в статистических моделях, порожденных фрактальными пуассоновскими процессами [Parallel title]Subject(s): полумарковская регрессия | фрактальные пуассоновские процессы | неасимптотическое оценивание | выбор модели | робастная оценка | оракульное неравенство | асимптотическая эффективностьGenre/Form: статьи в сборниках Online resources: Click here to access online
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Международная научная конференция "Робастная статистика и финансовая математика – 2020" 15-16 декабря 2020 г. : сборник статей С. 14-22Abstract: We study a non parametric estimation problem for regression models in continuous time with noises defined through non -Gaussian semi - Markov processes with jumps. Moreover, we assume that the jumps are modeled on the basis of the fractal Poisson processes with a memory in the increments. It should be noted that such models are very popular in stochastic financial markets and signal processing models. For such models we use the adaptive model selection methods developed in [2]. A sharp non-asymptotic oracle inequality for the robust risks is obtained and robust efficiency property for the Sobolev functional class is established.
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We study a non parametric estimation problem for regression models in continuous time with noises defined through non -Gaussian semi - Markov processes with jumps. Moreover, we assume that the jumps are modeled on the basis of the fractal Poisson processes with a memory in the increments. It should be noted that such models are very popular in stochastic financial markets and signal processing models. For such models we use the adaptive model selection methods developed in [2]. A sharp non-asymptotic oracle inequality for the robust risks is obtained and robust efficiency property for the Sobolev functional class is established.
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