偏正态条件下多元线性回归模型的统计推断及其应用  

Statistical Inference of Multiple Linear Regression Models with Skewed Normal Errors and Its Applications

作　　者：赵伟凯 杨兰军 戴琳[1,2] 吴刘仓[1,2] ZHAO Weikai;YANG Lanjun;DAI Lin;WU Liucang(School of Science,Kunming University of Science and Technology,Kunming 650500,China;Statistics Research Center,Kunming University of Science and Technology,Kunming 650500,China)

机构地区：[1]昆明理工大学理学院,云南昆明650500 [2]昆明理工大学统计学研究中心,云南昆明650500

出　　处：《应用数学》2024年第2期519-529,共11页Mathematica Applicata

基　　金：国家自然科学基金(12261051)。

摘　　要：本文考虑带偏正态随机项多元线性回归模型的统计推断问题.基于最大似然方法,本文所做的工作如下:1)证明了参数最大似然估计在n≥p+1条件下以概率1存在唯一;2)在唯一性条件下给出参数估计的一致性结论;3)在一致性的条件下研究了参数的渐近性质,给出参数的渐近分布.最后通过数值模拟说明了所提理论和方法的有效性.实例表明模型参数估计的渐近分布具有实际意义.In this paper,the statistical inference for multiple linear regression models with skewed normal errors is considered.Based on the maximum likelihood approach,the works are as follows:1)It is proved that the maximum likelihood estimators of the parameters exist with probability 1 under condition n≥p+1 and the uniqueness of the parameter estimators is discussed.The results of the numerical studies show that the estimators exist and are unique.2)The consistency of the estimators is given under the uniqueness assumption;3)The asymptotic distributions of the estimators are given under the uniqueness assumption.Finally,the validity of the proposed theory and method is illustrated by numerical simulations.The empirical examples show that the asymptotic distributions of the estimators are of practical significance.

关 键 词：偏正态分布 多元线性模型 最大似然估计 渐近正态性 

分 类 号：O212.1[理学—概率论与数理统计]