Kernel estimators of asymptotic variance for adaptive Markov chain Monte Carlo

Yves F. Atchadé

doi:10.1214/10-AOS828

Kernel estimators of asymptotic variance for adaptive Markov chain Monte Carlo

Probability 2011-05-17 v2 Statistics Theory Computation Statistics Theory

Authors: 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.

Keywords

adaptive markov chain monte carlo asymptotic variance kernel estimator long-run variance garch model bayesian logistic regression

Cite

@article{arxiv.0911.1164,
  title  = {Kernel estimators of asymptotic variance for adaptive Markov chain Monte Carlo},
  author = {Yves F. Atchadé},
  journal= {arXiv preprint arXiv:0911.1164},
  year   = {2011}
}

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

Kernel estimators of asymptotic variance for adaptive Markov chain Monte Carlo

Abstract

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