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

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.