A Note on Pooling Variances
研究了正态分布方差估计中，当两个样本是否来自同一总体不确定时，使用预检验决定是否合并样本，并分析了该预检验估计量的偏差和均方误差。
Abstract The estimation of variance in the normal distribution is studied under statistical inference based on conditional specification. When there are two samples available for estimating the variance and it is not certain whether the two samples are from the same population, the experimenter usually uses a test to resolve the uncertainty. When the test is not significant, the samples are pooled to obtain a pooled estimator; otherwise, the individual sample variance is used. The bias and mean squared error of such a preliminary test estimator are studied. It is shown that the preliminary test estimator has a smaller mean squared error than the usual unbiased estimator when the level of significance for the preliminary test is appropriately chosen.