On Stein's method, smoothing estimates in total variation distance and mixture distributions

FA Daly

Research output: Contribution to journalArticle (Academic Journal)peer-review

5 Citations (Scopus)

Abstract

In many settings it is useful to have bounds on the total variation distance between some random variable Z and its shifted version Z+1. For example, such quantities are often needed when applying Stein's method for probability approximation. This note considers one way in which such bounds can be derived, in cases where Z is either the equilibrium distribution of some birth–death process or the mixture of such a distribution. Applications of these bounds are given to translated Poisson and compound Poisson approximations for Poisson mixtures and the Pólya distribution.
Translated title of the contributionOn Stein's method, smoothing estimates in total variation distance and mixture distributions
Original languageEnglish
Pages (from-to)2228 - 2237
Number of pages10
JournalJournal of statistical planning and inference
Volume141
Issue number7
DOIs
Publication statusPublished - Jul 2011

Bibliographical note

Publisher: Elsevier

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