Asymptotic Efficiency of the Sample Mean in Markov Chain Monte Carlo Schemes
研究了可逆平稳马尔可夫链导出的单变量时间序列的自相关性质，并讨论了样本均值在子抽样中的渐近有效性，证明在强渐近平稳过程中样本均值在广泛线性估计类中渐近均方误差最小。
SUMMARY 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 integers l, its lth moment is the lth 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.