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April 2011 Kernel estimators of asymptotic variance for adaptive Markov chain Monte Carlo
Yves F. Atchadé
Ann. Statist. 39(2): 990-1011 (April 2011). DOI: 10.1214/10-AOS828

Abstract

We study the asymptotic behavior of kernel estimators of asymptotic variances (or long-run variances) for a class of adaptive Markov chains. The convergence is studied both in Lp and almost surely. The results also apply to Markov chains and improve on the existing literature by imposing weaker conditions. We illustrate the results with applications to the GARCH(1, 1) Markov model and to an adaptive MCMC algorithm for Bayesian logistic regression.

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Yves F. Atchadé. "Kernel estimators of asymptotic variance for adaptive Markov chain Monte Carlo." Ann. Statist. 39 (2) 990 - 1011, April 2011. https://doi.org/10.1214/10-AOS828

Information

Published: April 2011
First available in Project Euclid: 8 April 2011

zbMATH: 1219.62125
MathSciNet: MR2816345
Digital Object Identifier: 10.1214/10-AOS828

Subjects:
Primary: 60C05 , 60J10

Keywords: Adaptive Markov chain Monte Carlo , kernel estimators of asymptotic variance

Rights: Copyright © 2011 Institute of Mathematical Statistics

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Vol.39 • No. 2 • April 2011
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