Median-of-Means方法在偏度系数中的应用

Application of Median-of-Means Method in Skewness Coefficient

传统偏度系数的定义涉及样本均值和三阶矩,使其对离群值十分敏感。本文在偏度系数的估计中引入Median-of-Means方法,提出偏度系数的新估计量,并证明其相合性和渐近正态性。此外,基于经验似然方法提出一种新的偏度系数检验统计量,证明其渐近性质并进行数值模拟。结果表明,本文提出的估计量具有一定稳健性,检验统计量表现也优于传统方法。最后将所提出的估计与检验方法应用于实际数据分析发现,估计结果比较稳健,进一步表明原有的偏度系数估计方法并不适用。

The traditional definition of skewness coefficient involves the mean and third moment of the sample,which makes it very sensitive to outliers.We propose the Median-of-Means method and a new skewness coefficient estimator,and prove its consistency and asymptotic normality.We also propose a new test statistic of skewness coefficient based on the empirical likelihood method,prove the asymptotic nature of the test statistic and conduct the numerical simulation.Results show that the proposed method is robust,and the new test statistic also performs better than the traditional method.Finally,we apply the proposed methods to the actual data examples and find that the estimation results are relatively robust.The testing results further indicate that the original method for estimating the skewness coefficient is not applicable.