半正态误差下线性模型的补偿Lq极大似然估计量的渐近性质  

Asymptomatic properties of the penalized maximum Lq-likelihood estimators for the linear model with half-normal errors

作　　者：宋国文 马歌 胡宏昌 SONG Guo-wen;MA Ge;HU Hong-chang(College of Mathematics and Statistics, Hubei Normal University, Huangshi 435002,China)

机构地区：[1]湖北师范大学数学与统计学院,湖北黄石435002

出　　处：《湖北师范大学学报（自然科学版）》2020年第3期26-32,共7页Journal of Hubei Normal University：Natural Science

摘　　要：考虑半正态误差下线性回归模型yi=x^Tiβ+εi,利用正态分布N(0,λ2)密度函数作为补偿项,得到未知参数σ,λ,β的补偿Lq极大似然估计量,并讨论了估计量的相合性与渐近正态分布。这些结论推广了半正态误差下线性模型的极大似然估计量的相应结论。In this paper,we consider a linear regression model yi=x^Tiβ+εi with the half-normal errors.Using the normal distribution N(0,λ2)density function as a penalized term,we obtain the penalized maximum Lq-likelihood estimators of the unknown parametersσ,λandβ,and the consistency and asymptomatic distribution of the estimators are discussed.These conclusions generalize the corresponding conclusions of the maximum Lq-likelihood estimators for linear models with semi-normal errors.

关 键 词：半正态分布 线性回归模型 补偿Lq极大似然估计 相合性 渐近正态分布 

分 类 号：O212.1[理学—概率论与数理统计]