A weak law of large numbers for empirical measures via Stein's method
type: Item
instance of: scholarly article
title: A weak law of large numbers for empirical measures via Stein's method
zbMATH Open document ID: 0836.60019
published in: The Annals of Probability
publication date: 1996-04-09T00:00:00Z
review text: Let a family of random elements on a locally compact Hausdorff space be given. The weak law for the independent family is proved by using Stein's method. The range of this method is extended. The class of new results for empirical measures is provided here. The main result is extended for various kinds of dependences. An estimate for the rate of convergence is derived in terms of a Zolotarev metric (semimetric). Two examples (a dissociated family, an immigration-death process) are studied.
Mathematics Subject Classification ID: 60F05
Mathematics Subject Classification ID: 60G57
Mathematics Subject Classification ID: 60K25
Mathematics Subject Classification ID: 62G30
zbMATH DE Number: 796545
zbMATH Keywords: weak law of large numbers
zbMATH Keywords: Stein's method
zbMATH Keywords: empirical measures
Wikidata QID: Q57748059
author: Gesine Reinert
reviewed by: Pavel Froněk
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aop/1176988389
OpenAlex ID: W2079307214
DOI: 10.1214/AOP/1176988389
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description: scientific article; zbMATH DE number 796545