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 Electronic Journal of Probability > Vol. 13 (2008) > Paper 20 open journal systems 


Upper bounds for Stein-type operators

Fraser A Daly, University of Nottingham


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.


Full text: PDF

Pages: 566-587

Published on: April 12, 2008


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Electronic Journal of Probability. ISSN: 1083-6489