Kernel estimators of asymptotic variance for adaptive Markov chain Monte Carlo

Details Kernel estimators of asymptotic variance for adaptive Markov chain Monte Carlo Kernel estimators of asymptotic variance for adaptive Markov chain Monte Carlo

2009-11-06

arxiv.org/abs/0911.1164v2

Annals of Statistics 2011, Vol. 39, No. 2, 990-1011

Mathematics

Probability

Published in at http://dx.doi.org/10.1214/10-AOS828 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of

Scientific paper

10.1214/10-AOS828

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 $L^p$ 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 $\operatorname {GARCH}(1,1)$ Markov model and to an adaptive MCMC algorithm for Bayesian logistic regression.

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