多元t分布数据的局部影响分析  

Local Influence Analysis for the Data from Multivariate t Distribution

作　　者：解锋昌[1] 韦博成[2] 

机构地区：[1]南京农业大学数学系,南京210095 [2]东南大学数学系,南京210096

出　　处：《应用概率统计》2006年第2期173-183,共11页Chinese Journal of Applied Probability and Statistics

基　　金：国家自然科学基金(10371016);南京农业大学青年科技创新基金(KJ04020)资助项目

摘　　要：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．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,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．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．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.

关 键 词：多元T分布 局部影响 EM算法 加权扰动模型 正则曲率 

分 类 号：O212.1[理学—概率论与数理统计] TN915.1[理学—数学]