The Correlation Between Mean and Variance Estimators in Computer Simulation

Abstract

Consider the problem of estimating confidence intervals for the mean of a stationary stochastic process. Denote the point estimator for the process mean by , and let be an estimator for lim_{n −∞}nVar(), the variance parameter. In this paper, we derive expressions for the correlation between and for various variance parameter estimators and stochastic processes. Among the variance estimators under study are those arising from the methods of nonoverlapping batched means, overlapping batched means, and standardized time series. Also, we empirically examine the relationships between Corr( ) and Confidence interval estimator performance; we see that Corr( ) affects the symmetry of confidence interval coverage, but not necessarily the actual coverage.