Upper bounds for Stein-type operators

FA Daly

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

14 Citations (Scopus)

Abstract

We present sharp bounds on the supremum norm of DjSh for j>1, where D is the differential operator and S the Stein operator for the standard normal distribution. The same method is used to give analogous bounds for the exponential, Poisson and geometric distributions, with D replaced by the forward difference operator in the discrete case. We also discuss applications of these bounds to the central limit theorem, simple random sampling, Poisson-Charlier approximation and geometric approximation using stochastic orderings.
Translated title of the contributionUpper bounds for Stein-type operators
Original languageEnglish
Pages (from-to)566 - 587
Number of pages22
JournalElectronic Journal of Probability
Volume13
Publication statusPublished - Apr 2008

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