偏正态数据下联合位置、尺度、偏度模型的统计诊断  

Statistical Diagnostics for Joint Location,Scale and Skewness Models with Skew-normal Data

作　　者：吴刘仓[1] 聂兴锋 郑桂芬 WU Liu-cang;NIE Xing-feng;ZHENG Gui-fen(Faculty of Science,Kunming University of Science and Technology,Kunming 650093)

机构地区：[1]昆明理工大学理学院,昆明650093

出　　处：《工程数学学报》2021年第2期180-194,共15页Chinese Journal of Engineering Mathematics

基　　金：国家自然科学基金(11861041;11261025).

摘　　要：在经济学、生物医学、环境科学等领域存在这样一类数据,异方差、含有多个异常点或强影响点、且存在偏斜.针对这类数据,本文研究了偏正态数据下联合位置、尺度、偏度模型的统计诊断.首先将正态下Pena距离推广到了偏正态,故适用范围更广.其次利用似然距离、Cook距离、Pena距离以及局部影响分析等诊断方法进行比较,得到了在一定条件下Pena距离相对优于Cook距离和似然距离.最后,通过随机模拟试验研究和实例分析,表明本文提出的理论和方法是科学合理的.There is such a kind of data as heteroscedasticity,contains multiple outliers or strong influence points and skewness in the fields of economy,biomedicine and environmental science.Based on the data,this paper is concerned with the statistical diagnosis of joint location,scale and skewness models.Firstly,the Pena distance under the normal distribution is extended to the skew-normal distribution,so this method has a more widely application.Secondly,the likelihood distance,Cook distance,Pena distance and local influence analysis are used to compare the diagnostic methods,and Pena distance is better than Cook and likelihood distance under certain conditions.Finally,through Monte Carlo simulation experiments and a real data analysis,it indicates that the theories and proposed methods in this paper are scientific and reasonable.

关 键 词：Pena距离 偏正态分布 联合位置、尺度、偏度模型 统计诊断 

分 类 号：O212.1[理学—概率论与数理统计]