Sergey Bobkov, Michel Ledoux One-Dimensional Empirical Measures, Order Statistics, and Kantorovich Transport Distances 9781470436506

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Автор: Sergey Bobkov, Michel Ledoux
Название: One-Dimensional Empirical Measures, Order Statistics, and Kantorovich Transport Distances
ISBN: 9781470436506
Издательство: Mare Nostrum (Eurospan)
Классификация:

Вероятность и статистика

ISBN-10: 1470436507
Обложка/Формат: Paperback
Страницы: 126
Вес: 0.28 кг.
Дата издания: 30.12.2019
Серия: Memoirs of the american mathematical society
Язык: English
Размер: H 254 X W 178
Читательская аудитория: Professional and scholarly
Ключевые слова: Probability & statistics
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Поставляется из: Англии
Описание: This work is devoted to the study of rates of convergence of the empirical measures $\mu_{n} = \frac {1}{n} \sum_{k=1}^n \delta_{X_k}$, $n \geq 1$, over a sample $(X_{k})_{k \geq 1}$ of independent identically distributed real-valued random variables towards the common distribution $\mu$ in Kantorovich transport distances $W_p$. The focus is on finite range bounds on the expected Kantorovich distances $\mathbb{E}(W_{p}(\mu_{n},\mu ))$ or $\big [ \mathbb{E}(W_{p}^p(\mu_{n},\mu )) \big ]^1/p$ in terms of moments and analytic conditions on the measure $\mu $ and its distribution function. The study describes a variety of rates, from the standard one $\frac {1}{\sqrt n}$ to slower rates, and both lower and upper-bounds on $\mathbb{E}(W_{p}(\mu_{n},\mu ))$ for fixed $n$ in various instances. Order statistics, reduction to uniform samples and analysis of beta distributions, inverse distribution functions, log-concavity are main tools in the investigation. Two detailed appendices collect classical and some new facts on inverse distribution functions and beta distributions and their densities necessary to the investigation.
Дополнительное описание: Probability and statistics

One-Dimensional Empirical Measures, Order Statistics, and Kantorovich Transport Distances, Sergey Bobkov, Michel Ledoux