Stein's method of exchangeable pairs for absolutely continuous, univariate distributions with applications to the Polya urn model

2012/07/02 by Döbler, Christian
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1207.0533

Abstract

We propose a way of finding a Stein type characterization of a given absolutely continuous distribution μ on \R which is motivated by a regression property satisfied by an exchangeable pair (W,W') where \calL(W) is supposed or known to be close to μ. We also develop the exchangeable pairs approach within this setting. This general procedure is then specialized to the class of Beta distributions and as an application, a convergence rate for the relative number of drawn red balls among the first n drawings from a Polya urn is computed.

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