响应数据缺失下一般线性复合分位数光滑经验似然估计  

Smoothed Empirical Likelihood Method of General Linear Composite Quantile Regression Model with Missing Response Data

作　　者：黄婉娟 罗双华[1] 张成毅 HUANG Wanjuan;LUO Shuanghua;ZHANG Chengyi(School of Science,Xi'an Polytechnic University,Xi'an 710048,Shanxi;School of Economics and Finance,Xi'an Jiaotong University,Xi'an 710049,Shanxi)

机构地区：[1]西安工程大学理学院,陕西西安710048 [2]西安交通大学经济与金融学院,陕西西安710049

出　　处：《四川师范大学学报（自然科学版）》2023年第5期628-637,共10页Journal of Sichuan Normal University（Natural Science）

基　　金：陕西省自然科学基金(2020JM571和2021JM-002)。

摘　　要：由于分位数回归模型的损失函数不光滑,所得参数估计的效率不高,为提高参数估计的效率,首先提出复合分位数光滑经验对数似然比,包括完全数据复合分位数光滑经验对数似然比、加权复合分位数光滑经验对数似然比和插值复合分位数光滑经验对数似然比,并在一定条件下证明了它们都是服从渐近卡方分布的.其次,根据该似然比构造了回归参数的置信区间,并证明了复合分位数光滑经验似然估计量是渐近正态的.最后,通过数值模拟实验说明了所得估计的有效性.Since the loss function of quantile regression model with missing response data is not smooth,the efficiency of parameter estimation is not high.In order to improve the efficiency of parameter estimation,the smoothed empirical log likelihood ratio of composite quantile regression model is firstly proposed in this paper,including the smoothed empirical log likelihood ratio of composite quantile regression model with complete data,weighted data and imputation,and the constructed smoothed empirical log likelihood ratio is proved to obey the asymptotic Chi-square distribution under certain conditions.Secondly,the confidence interval of regression parameter is constructed according to the likelihood ratio,and the empirical likelihood estimator is proved to be asymptotically normality.Finally,the performance of the estimators is assessed by numerical simulation.

关 键 词：缺失数据 复合分位数回归模型 光滑经验对数似然比 渐近正态性 

分 类 号：O212[理学—概率论与数理统计]