Properties of Standardized Time Series Weighted Area Variance Estimators
研究连续时间平稳随机过程中样本均值的方差估计，提出加权面积方差估计量，其渐近偏差低于其他常用估计量，并基于此构造渐近有效的置信区间，有时覆盖率更接近名义值。
We 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 1990) by using the theory of standardized time series to investigate weighted generalizations of Schruben's area variance estimator. We find a simple expression for the bias of the weighted area variance estimator, and we give weights which yield variance estimators with lower asymptotic bias than certain other popular estimators. We 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, we show that the new CIEs sometimes yield coverages which are closer to the nominal value.