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arXiv · 0911.1164

Kernel estimators of asymptotic variance for adaptive Markov chain Monte Carlo

Yves F. Atchadé
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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 $L^p$ 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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BibTeXRIS

Yves F. Atchadé. 2011-05-16. Kernel estimators of asymptotic variance for adaptive Markov chain Monte Carlo. https://doi.org/10.1214/10-aos828

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