多元$t$分布数据的局部影响分析

对于多元$t$分布数据, 直接应用其概率密度进行影响分析是困难的\bd 本文通过引入服从Gamma分布的权重, 将其表示为特定多元正态分布的混合\bd 在此基础上, 进而将权重视为缺失数据, 引入EM算法; 从而利用基于完全数据似然函数的条件期望进行局部影响分析\bd 本文进一步系统研究了加权扰动模型下的局部影响分析, 得到了相应的诊断统计量; 并通过两个实例说明了这种方法的有效性.

Local Influence Analysis for the Data from Multivariate $t$ Distribution

For the data from multivariate t distribution, it is hard to do influence analysis based on its probability density function. But it can be considered as a particular Gaussian mixture by introducing the weight from the Gamma distribution. Based on this fact, we treat the weight as the missing data and develop the local influence analysis for the data from multivariate t distribution based on the conditional expectation of the complete-data log-likelihood function in the EM algorithm. The local influence based on the case-weights perturbation is discussed in detail and two numerical examples are given to illustrate our results.