基于加权复合分位数回归的变系数部分线性模型的稳健经验似然估计  

Robust empirical likelihood estimation for variable partially linear models via weighted composite quantile regression

作　　者：叶芸莉 赵培信[1,2] YE Yunli;ZHAO Peixin(College of Mathematics and Statistics,Chongqing Technologyand Business University,Chongqing 400067,China;Chongqing Key Laboratory of Social Economy and Applied Statistics,Chongqing 400067,China)

机构地区：[1]重庆工商大学数学与统计学院,重庆400067 [2]经济社会应用统计重庆市重点实验室,重庆400067

出　　处：《齐鲁工业大学学报》2024年第2期73-80,共8页Journal of Qilu University of Technology

基　　金：国家社会科学基金一般项目(18BTJ035);重庆市自然科学基金面上项目(cstc2020jcyj-msxmX0006)。

摘　　要：研究了变系数部分线性模型的稳健经验似然推断问题。利用加权复合分位数回归以及经验似然方法,并结合基于矩阵QR分解的正交投影技术,对模型的参数分量提出了一种基于加权复合分数回归的经验似然估计方法。理论证明了提出的经验对数似然比函数渐近服从卡方分布,得到参数分量的置信区间。该估计方法中引入了基于矩阵QR分解的正交投影技术,保证对模型的参数分量进行估计时不会受到非参数分量估计精度的影响,因此具有较好的稳健性和有效性。The robust empirical likelihood inferences for varying coefficient partially linear models are studied.Using weighted composite quantile regression and empirical likelihood method,combined with orthogonal projection technology based on matrix QR decomposition,an empirical likelihood estimation method based on weighted composite fractional regression is proposed for parameter components of the model.Theoretical proof has been provided that the proposed empirical logarithmic likelihood ratio function asymptotically follows a chi square distribution,thereby constructing confidence intervals for parameter components.The orthogonal projection technique based on matrix QR decomposition is introduced in this estimation method,which ensures that the estimation of parameter components is not affected by the estimation accuracy of nonparametric components,so it has better robustness and effectiveness.

关 键 词：加权复合分位数回归 部分线性变系数模型 稳健经验似然 正交投影 

分 类 号：O212.7[理学—概率论与数理统计]