Properties of standardized time series weighted area variance estimators

The authors wish to estimate the variance of the sample mean from a continuous-time stationary stochastic process. This article expands on the results of a technical note (Goldsman and Schruben) by using the theory of standardized time series to investigate weighted generalizations of Schruben’s area variance estimator. The authors find a simple expression for the bias of the weighted area variance estimator, and they give weights which yield variance estimators with lower asymptotic bias than certain other popular estimators. The authors use the weighted area variance estimators to derive asymptotically valid confidence interval estimators (CIEs) for the mean of a stationary stochastic process. Although the weighted area CIEs have the same asymptotic expected value and variance of the length as Schruben’s area CIE, they show that the new CIEs sometimes yield coverages which are closer to the nominal value.