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Markov chain Monte Carlo (MCMC) is a simulation method commonly used forestimating expectations with respect to a given distribution. We considerestimating the covariance matrix of the asymptotic multivariate normaldistribution of a vector of sample means. Geyer (1992) developed a Monte Carloerror estimation method for estimating a univariate mean. We propose a novelmultivariate version of Geyer's method that provides an asymptotically validestimator for the covariance matrix and results in stable Monte Carloestimates. The finite sample properties of the proposed method are investigatedvia simulation experiments.

Multivariate initial sequence estimators in Markov chain Monte Carlo