The asymptotic distribution of the bootstrap sample mean of an infinitesimal array
type: Item
instance of: scholarly article
title: The asymptotic distribution of the bootstrap sample mean of an infinitesimal array
zbMATH Open document ID: 0907.62018
DOI: 10.1016/S0246-0203(98)80012-5
published in: Annales de l'Institut Henri Poincaré. Probabilités et Statistiques
publication date: 1999-03-08T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/77593
review text: The paper offers asymptotic results for the bootstrap of the sample mean given by an infinitesimal array of rowwise i.e.d. random variables with convergent partial sums. It is known that the ordinary bootstrap works if the central limit theorem holds for the underlying array, see for instance \textit{E. Mammen} [When does bootstrap work? Asymptotic results and simulations. (1992; Zbl 0760.62038)]. If the limit law has a nontrivial Poisson part then the bootstrap statistic may have a data-dependent limit law. These laws are typically infinitely divisible. Results of this type are also discussed when the bootstrap sample size \(m_n\) and the original sample size \(k_n\) of the data fulfill \(m_0= o(k_n)\) or \(k_n= o(m_n)\) and \(\min (k_n,m_n) \to \infty\). The results and the methods of proof are very interesting.
Mathematics Subject Classification ID: 62E20
Mathematics Subject Classification ID: 62F12
Mathematics Subject Classification ID: 60F05
Mathematics Subject Classification ID: 62G09
zbMATH DE Number: 1156742
zbMATH Keywords: bootstrap of sample means
zbMATH Keywords: infinitely divisible limit law
zbMATH Keywords: Poisson random variable
zbMATH Keywords: conditional limit theorem
zbMATH Keywords: central limit theorem
author: Juan Antonio Cuesta-Albertos
author: Carlos Matrán
reviewed by: Arnold Janssen
MaRDI profile type: Publication
OpenAlex ID: W2034936405
description: scientific article; zbMATH DE number 1156742