%0 Journal Article
%T Kernel estimators of asymptotic variance for adaptive Markov chain Monte Carlo
%A Yves F. Atchad¨¦
%J Mathematics
%D 2009
%I arXiv
%R 10.1214/10-AOS828
%X 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.
%U http://arxiv.org/abs/0911.1164v2