Asymptotic and finite-sample correlations between OBM estimators

Linear combinations of estimators offer a variety of good computational and statistical properties. The values of the optimal linear-combination weights depend upon the estimators' covariances. We investigate the asymptotic covariances and correlations between overlapping-batch-means estimators of the variance of the sample mean when applied to a common sample from a stationary finite-order moving-average data process. After reviewing the asymptotic formulas, we report a Monte Carlo study that suggests that the asymptotic correlation formula provides a good approximation to the true finite-sample correlation if (1) the sample size n is at least several multiples of /spl gamma/0 and (2) the both batch sizes are between /spl gamma/0 and n/2, where /spl gamma/0 is the sum of all autocorrelation.