@article{EJP479,
author = {Fraser Daly},
title = {Upper Bounds for Stein-Type Operators},
journal = {Electron. J. Probab.},
fjournal = {Electronic Journal of Probability},
volume = {13},
year = {2008},
keywords = {Stein-type operator; Stein's method; central limit theorem; Poisson-Charlier approximation; stochastic ordering},
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.},
pages = {no. 20, 566-587},
issn = {1083-6489},
doi = {10.1214/EJP.v13-479},
url = {http://ejp.ejpecp.org/article/view/479}}