新权值的权估计及其方差分析

摘要

运用Zhang处理方差的技巧来研究均值的估计问题,对加权平均的均值, 尤其是解决测量样本量不同的样本问题,提出了一个新的具有无偏性的估计, 并且通过模拟说明, 在多数情况下,特别是当样本量很大时, 这个新的估计具有较小的偏差和均方误差. 然后,针对这个均值估计的方差, 又给出了一个合适的估计,而且说明其稳健性. 最后将此估计与bootstrap方法所得到的结果进行比较.%The technique Zhang used to estimate variance was used to research the estimation of mean values. In particular, when the sample size was different, a new unbiased estimator of the weighted mean was proposed. In most cases, especially where the sample size was large, it was shown that the new estimator has smaller biases and smaller mean square errors. Then a proper estimator of the variance of this weighted mean was given, which was robust. Finally the estimator of variance of the new modified weighed mean was compared with the results by bootstrap.