零一膨胀泊松模型的似然检验及模型比较  

Likelihood Test and Model Comparison of Zero-and-one-inflated Poisson Model

作　　者：刘娱 安博文 田茂再[1,2,3,4] Liu Yu;An Bowen;Tian Maozai(School of Statistics and Data Sciences,Xinjiang University of Finance and Economics,Urumqi 830012,China;School of Statistics,Renmin University of China,Beijing 100872,China;Center for Applied Statistics,Renmin University of China,Beijing 100872,China;School of Statistics,Lanzhou University of Finance and Economics,Lanzhou 730020,China)

机构地区：[1]新疆财经大学统计与数据科学学院,乌鲁木齐830012 [2]中国人民大学统计学院,北京100872 [3]中国人民大学应用统计科学研究中心,北京100872 [4]兰州财经大学统计学院,兰州730020

出　　处：《统计与决策》2021年第13期20-24,共5页Statistics & Decision

基　　金：国家自然科学基金资助项目(11861042);新疆财经大学研究生科研创新项目(XJUFE2020K006)。

摘　　要：针对复杂计数数据中出现零值与一值同时膨胀导致难以确定数据类型的问题,文章基于零一膨胀泊松分布模型,分别构建了Wald检验、LR检验以及Score检验的检验统计量。在实际应用中为推广零一膨胀泊松回归模型,采用EM算法对参数估计值及置信区间进行求解。对暴风雪发生次数进行分析,其检验统计量的结果证明了该数据存在零值与一值同时膨胀,并确定了适用于此数据的最优模型为零一膨胀泊松模型。Aiming at the problem that it is difficult to determine the data type due to the simultaneous inflation of 0 and 1 values in complex counting data, this paper constructs Wald test, LR test and Score test statistics based on zero-and-one-inflated Poisson distribution model. In practical application, the EM algorithm is used to solve the parameter estimation values and confidence interval in order to popularize the zero-and-one-inflated Poisson regression model. The paper also makes analyses on the occurrence times of snowstorms. The results of the test statistics prove that the data has simultaneous inflation of 0 and 1 values,and determine that the optimal model suitable for this data is the zero-and-one-inflated Poisson model.

关 键 词：零一膨胀泊松模型 WALD检验 LR检验 SCORE检验 极端天气 

分 类 号：O21[理学—概率论与数理统计]