Poisson and Gaussian approximation of weighted local empirical processes
type: Item
instance of: scholarly article
title: Poisson and Gaussian approximation of weighted local empirical processes
zbMATH Open document ID: 0911.60004
DOI: 10.1016/S0304-4149(97)00055-0
author: John H. J. Einmahl
published in: Stochastic Processes and their Applications
publication date: 1999-01-14T00:00:00Z
review text: Let \(S\) be a complete separable metric space with the Borel field \(\mathcal B .\) Let \(X_{n,i}\), \(i=1,\dots , n\), be independent identically distributed random elements with values in \((S,\mathcal B).\) Consider the empirical measure \(P_n(B) = \frac {1}{n}\sum _{i=1}^n \mathbb I _B (X_{n,i})\), \(B \in \mathcal B\), and the true probability measure \(P_{(n)}(B) = \mathbb P(X_{n,i} \in B),\;B\in \mathcal B. \) Poisson and Gaussian weighted approximations of the local empirical process defined by means of \(P_n(A) - P_{(n)}(A)\), \(A \in \mathcal A \subset \mathcal B\), are studied. It is shown that results for weighted local empirical processes indexed by a set obtained in the paper generalize many previous results on weighted empirical processes, that are now formulated as corollaries.
reviewed by: Zuzana Prášková
Mathematics Subject Classification ID: 60F05
Mathematics Subject Classification ID: 62E20
Mathematics Subject Classification ID: 62G30
Mathematics Subject Classification ID: 60F17
zbMATH DE Number: 1240040
zbMATH Keywords: extreme value theory
zbMATH Keywords: local empirical process
zbMATH Keywords: tail empirical process
zbMATH Keywords: Poisson approximation
zbMATH Keywords: Gaussian approximation
MaRDI profile type: Publication
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full work available at URL: s0304-4149(97)00055-0
OpenAlex ID: W2130672055
description: scientific article; zbMATH DE number 1240040