KERNEL ESTIMATORS OF ASYMPTOTIC VARIANCE FOR ADAPTIVE MARKOV CHAIN MONTE CARLO

• 成果类型: Article
• 署名作者: Atchade, Yves F.
• 署名单位: University of Michigan System; University of Michigan
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/10-AOS828
• 发表日期: 2011
• 页码: 990-1011
• 关键词: Consistency; ergodicity; heteroskedasticity

摘要

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 GARCH(1, 1) Markov model and to an adaptive MCMC algorithm for Bayesian logistic regression.