  Markov chain Monte Carlo (MCMC) is a simulation method commonly used for
estimating expectations with respect to a given distribution. We consider
estimating the covariance matrix of the asymptotic multivariate normal
distribution of a vector of sample means. Geyer (1992) developed a Monte Carlo
error estimation method for estimating a univariate mean. We propose a novel
multivariate version of Geyer's method that provides an asymptotically valid
estimator for the covariance matrix and results in stable Monte Carlo
estimates. The finite sample properties of the proposed method are investigated
via simulation experiments.
