西北师范大学学报（自然科学版）2019，Vol.55Issue(1)：26-34,9.DOI:10.16783/j.cnki.nwnuz.2019.01.005
未知误差分布下线性回归模型的非参数自适应估计
Nonparametric adaptive estimation of linear regression models with the unknown error distribution
摘要
Abstract
For normally distributed errors, the maximum likelihood estimate (MLE) is equivalent to the least squares estimate (LSE) in linear regression models.In the absence of Gaussianity, MLE is more effective than LSE.However, the error distribution is generally unknown, and MLE is infeasible.Anonparametric adaptive method is proposed to estimate parameters in a linear regression model with unknown error distribution, the resulting estimator is asymptotically as efficient as the oracle MLE that the error distribution is known.A profile likelihood ratio test for regression parameters is also proposed.关键词
线性回归模型/极大似然估计/Newton-Raphson算法/假设检验Key words
linear regression model/MLE/Newton-Raphson algorithm/hypothesis testing分类
数理科学引用本文复制引用
龙伟芳,叶绪国..未知误差分布下线性回归模型的非参数自适应估计[J].西北师范大学学报（自然科学版）,2019,55(1):26-34,9.基金项目
国家自然科学基金资助项目(11701286) （11701286）
贵州省教育厅青年科技人才成长项目(黔教合KY字[2018]363) （黔教合KY字[2018]363）
凯里学院校级重点课题项目(Z1701,Z1505) （Z1701,Z1505）
