极端值影响下总体均值估计量的调整

The Adjustment of Mean Estimation with Extreme Value

在含有极端值总体中,由于样本均值不具有耐抗性,往往难以代表"平均水平",因此样本方差也难以有效衡量离散程度。在简单随机抽样假设下,可以构造一个考虑极大值和极小值对样本均值大小影响作用不同时的调整均值估计量,并给出了其期望与方差。根据方差最小原则,确定估计量中的参数。随后的统计模拟比较了各种估计量的表现,结果表明:调整的估计量是稳健的和有效的。

In the presence of extreme value of the population, since the sample mean is not robust, it＇s often difficult to represent the ＂average＂ Therefore sample variance is no longer an effective estimate of the population dispersion. Based on the assumption of SRS, we construct an adjusted estimate of population mean which consider maximum and minimum extreme value, then we discuss its expectation and variance. In accordance with the principle of minimum variance, we determine the parameters of the estimation. Monte Carlo method is applied to test the robustness and efficiency of the estimation.