Asymptotic Efficiency of the Sample Mean in Markov Chain Monte Carlo Schemes
Journal of the Royal Statistical Society: Series B (Statistical Methodology) · 1996 · Volume 58 · Issue 3
DOI: 10.1111/j.2517-6161.1996.tb02098.x
Abstract
In many cases, a univariate time series derived from a time reversible stationary Markov chain has the property that there is a distribution function on [–1, 1] ([0, 1]) such that, for all non-negative integersl, itslth moment is thelth lag autocorrelation of the time series. We discuss some consequences of this property. Effects of the asymptotic efficiency of the sample mean on the efficiency of subsampling a stationary Markov chain are discussed. The stationarity assumption is then relaxed. We show that under certain regularity conditions the sample mean of a strongly asymptotically stationary process is asymptotically efficient in that it has the smallest mean-square error asymptotically in a broad class of linear estimators.
Keywords
autocorrelation, gibbs sampling, ρ-mixing, spectral density function, subsampling
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