Institute of Mathematical Statistics Lecture Notes - Monograph Series

Use of exchangeable pairs in the analysis of simulations

Charles Stein, Persi Diaconis, Susan Holmes, and Gesine Reinert

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Abstract

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.

Chapter information

Source
Persi Diaconis and Susan Holmes, eds., Stein's Method: Expository Lectures and Applications (Beachwood, Ohio, USA: Institute of Mathematical Statistics, 2004) , 1-25

Dates
First available in Project Euclid: 28 November 2007

Permanent link to this document
https://projecteuclid.org/euclid.lnms/1196283797

Digital Object Identifier
doi:10.1214/lnms/1196283797

Mathematical Reviews number (MathSciNet)
MR2118600

Rights
Copyright © 2004, Institute of Mathematical Statistics

Citation

Stein, Charles; Diaconis, Persi; Holmes, Susan; Reinert, Gesine. Use of exchangeable pairs in the analysis of simulations. Stein's Method, 1--25, Institute of Mathematical Statistics, Beachwood, Ohio, USA, 2004. doi:10.1214/lnms/1196283797. https://projecteuclid.org/euclid.lnms/1196283797


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