Large ball probabilities in statistical inference

Автор: Ulyanov V.V.
Сборник: 12th International Vilnius Conference on Probability Theory and Mathematical Statistics and 2018 IMS Annual Meeting on Probability and Statistics. Abstracts
Серия: без серии
Тезисы
Год издания: 2018
Место издания: VTeX, Vilnius Vilnius, Lithuania
Первая страница: 178
Последняя страница: 178
Аннотация: We derive tight non-asymptotic bounds for the Kolmogorov distance between the probabilities of two Gaussian elements to hit a ball in a Hilbert space. The key property of these bounds is that they are dimension-free and depend on the nuclear (Schatten-one) norm of the difference between the covariance operators of the elements and on the norm of the mean shift. The obtained bounds significantly improve the bound based on Pinsker's inequality via the Kullback-Leibler divergence. We also establish an anti-concentration bound for a squared norm of a non-centered Gaussian element in a Hilbert space. All bounds are sharp and cannot be improved in general. We present a number of examples motivating our results and applications of the obtained bounds to statistical inference and to high-dimensional CLT.
Добавил в систему: Ульянов Владимир Васильевич

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