基于等效残差积探测粗差的方差-协方差分量估计

Equivalent Residual Product Based Outlier Detection for Variance and Covariance Component Estimation

已有方差-协方差分量估计(VCE)的粗差探测是对残差检验,而VCE的本质是利用残差的二阶量来估计它的二阶中心矩,因此更合理的方法应该对残差二阶量检验。由最小二乘残差估值导出了一组服从标准正态分布的等效残差;然后从等效残差的VCE基本方程出发,分别采用χ2统计量和正态积Np统计量检验等效残差的平方及其乘积。结果表明,采用正态分布统计量以置信水平α检验等效残差相当于采用χ2统计量以相等的置信水平检验等效残差的平方,而以小于α的置信水平采用Np统计量检验等效残差的乘积。比较基于残差和残差二阶量的粗差剔除的VCE结果,两者的方差分量估值等价,但基于残差二阶量粗差剔除的VCE能更有效地估计协方差。

The existing outlier detection methods in variance-covariance component estimation（VCE） are based on the residuals.However,the essential inputs of VCE are the second-order values of residuals and,thus it is more reasonable to carry out the outlier detection using these second-order values directly.In this paper,starting with the fundament VCE equations based on equivalent residuals with standard normal distribution,we propose a new method to detect the outliers of VCE inputs where the chi-square（χ2） and normal product（Np） statistics are used to test the residual squares and their products for one another with a given confidence probability,respectively.The results show that if a confidence probability α is used to detect outliers with normal distribution statistic in residual domain,it is equivalent to test the residual squares with the same confidence probability using χ2 statistic but to test the products of residuals with a confidence probability smaller than α.Therefore,the variance estimates are equivalent using residual based or χ2 based outlier detection,but the better covariance estimates are achievable using Np based outlier detection than residual based one.