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

Abstract

We propose a way of finding a Stein type characterization of a given absolutely continuous distribution $\mu$ on $\mathbb{R}$ which is motivated by a regression property satisfied by an exchangeable pair $(W,W^{\prime })$ where $\calL(W)$ is supposed or known to be close to $\mu$. 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.

Some typos have been corrected and Proposition 3.2 has been delivered in addition

References in corpus (1)

• Zero biasing and growth processes

Cited by in corpus (2)

• A rate of convergence for the arcsine law by Stein's method
• Stein's density approach and information inequalities