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2008 Upper Bounds for Stein-Type Operators
Fraser Daly
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Electron. J. Probab. 13: 566-587 (2008). DOI: 10.1214/EJP.v13-479

Abstract

We present sharp bounds on the supremum norm of $\mathcal{D}^jSh$ for $j\geq2$, where $\mathcal{D}$ 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 $\mathcal{D}$ 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.

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Fraser Daly. "Upper Bounds for Stein-Type Operators." Electron. J. Probab. 13 566 - 587, 2008. https://doi.org/10.1214/EJP.v13-479

Information

Accepted: 12 April 2008; Published: 2008
First available in Project Euclid: 1 June 2016

zbMATH: 1196.60032
MathSciNet: MR2399291
Digital Object Identifier: 10.1214/EJP.v13-479

Subjects:
Primary: 60F05
Secondary: 60J80, 62E17

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Vol.13 • 2008
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