Kernel estimators of asymptotic variance for adaptive Markov chain Monte Carlo.(English)Zbl 1219.62125

Summary: 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.

MSC:

 62M05 Markov processes: estimation; hidden Markov models 60J22 Computational methods in Markov chains 62G05 Nonparametric estimation 62G20 Asymptotic properties of nonparametric inference 65C40 Numerical analysis or methods applied to Markov chains 60F05 Central limit and other weak theorems
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