Kernel estimators of asymptotic variance for adaptive Markov chain Monte Carlo

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

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)

References in corpus (4)

• On the ergodicity properties of some adaptive MCMC algorithms
• Batch means and spectral variance estimators in Markov chain Monte Carlo
• Renewal theory and computable convergence rates for geometrically ergodic Markov chains
• On the ergodicity of the adaptive Metropolis algorithm on unbounded domains

Cited by in corpus (7)

• Component-Wise Markov Chain Monte Carlo: Uniform and Geometric Ergodicity under Mixing and Composition
• Markov Chain Monte Carlo confidence intervals
• Strong Consistency of Multivariate Spectral Variance Estimators
• Neuronized Priors for Bayesian Sparse Linear Regression
• Limit Theorems for quadratic forms of Markov Chains
• Batch size selection for variance estimators in MCMC
• Analyzing MCMC Output