双幂变换下参数极大似然估计的精确分布研究  

A study of the accurate distribution of the maximum likelihood estimates for parameters under dual power transformation

作　　者：丘甜 华伟平[3] 李新光[1] 白鹏[2] 

机构地区：[1]武夷学院商学院,福建武夷山354300 [2]云南财经大学统计与数学学院,云南昆明650221 [3]武夷学院生态与工程学院,福建武夷山354300

出　　处：《云南民族大学学报（自然科学版）》2016年第3期246-250,共5页Journal of Yunnan Minzu University:Natural Sciences Edition

基　　金：福建省社会科学规划项目(FJ2015C241);福建省中青年教师教育科研项目(JAS150608);武夷学院校教科研基金项目(XD201402)

摘　　要：在双幂变换下,使用极大似然估计方法估计正态线性回归模型中的变换参数,并研究其精确分布.给出了极大似然估计的精确分布函数,并通过模拟研究表明了,其分布不仅依赖于变换参数取值,还与方差和回归系数的取值密切相关;得到极大似然估计是一奇异随机变量,不具有密度函数的结论.为双幂变换的应用提供了很重要的理论依据.Under dual power transformation, this paper uses the maximum likelihood estimation to estimate the pa- rameters in the normal linear regression model and then studies their accurate distribution. It provides the accurate distribution function of the maximum likelihood estimates. And the simulation study shows that the distribution not only depends on the value of parameters but also is closely related to the value of variance and regression coeffi- cients. It has reached the conclusion that the maximum likelihood estimate, which is a singular random variable, has no density function, which provides a very important theoretical basis for the use of dual power transformation.

关 键 词：双幂变换 精确分布 正态线性回归模型 极大似然估计 模拟研究 

分 类 号：O212[理学—概率论与数理统计]