Use of exchangeable pairs in the analysis of simulations

Abstract

<!-- *** Custom HTML *** --> The method of exchangeable pairs has emerged as an important tool in proving limit theorems for Poisson, normal and other classical approximations. Here the method is used in a simulation context. We estimate transition probabilitites from the simulations and use these to reduce variances. Exchangeable pairs are used as control variates. Finally, a general approximation theorem is developed that can be complemented by simulations to provide actual estimates of approximation errors.

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