| 基于协变量缺失的Horvitz-Thompson加权分位回归估计方法 |
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| 引用本文： | 储昭霁,邰凌楠,熊巍,郭旭,田茂再.基于协变量缺失的Horvitz-Thompson加权分位回归估计方法[J].数学研究及应用,2021,41(3):303-322. |
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| 作者姓名： | 储昭霁 邰凌楠 熊巍 郭旭 田茂再 |
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| 作者单位： | 中国人民大学统计学院, 北京 100872;中国人民大学统计学院, 北京 100872; 对外经济贸易大学统计学院, 北京 100029;中国人民大学统计学院, 北京 100872; 北京师范大学统计学院, 北京100875;中国人民大学统计学院, 北京 100872; 新疆医科大学医学工程与技术系, 新疆 乌鲁木齐 830011; 新疆财经大学统计与信息学院, 新疆 乌鲁木齐 830012 |
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| 基金项目： | 国家自然科学基金(Grant No.11861042), 中国统计研究计划(Grant No.2020LZ25). |
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| 摘 要： | 含有协变量缺失的数据缺失问题是现代统计分析中的热点之一.当缺失数据中同时存在厚尾,偏斜和异方差问题时则更加难以处理.为此,本文提出一种逆概率加权分位回归估计来研究响应和协变量之间的关系.与经典估计方法相比具有明显优势,一方面,该估计量使用了所有可用的数据,并且允许缺失的协变量与响应高度相关;另一方面,该估计量在所有分位数水平上满足一致性和渐近正态性.通过模拟验证了该方法的在有限样本下的有效性,进一步将该方法推广到线性多元回归模型和非参数回归模型.
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| 关 键 词： | 稳健分位回归 缺失协变量 选择概率 核密度估计 加权方法 |
| 收稿时间： | 2020/3/17 0:00:00 |
| 修稿时间： | 2021/1/28 0:00:00 |
The Horvitz-Thompson Weighting Method for Quantile Regression Estimation in the Presence of Missing Covariates |
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| Zhaoji CHU,Lingnan TAI,Wei XIONG,Xu GUO,Maozai TIAN.The Horvitz-Thompson Weighting Method for Quantile Regression Estimation in the Presence of Missing Covariates[J].Journal of Mathematical Research with Applications,2021,41(3):303-322. |
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| Authors: | Zhaoji CHU Lingnan TAI Wei XIONG Xu GUO Maozai TIAN |
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| Institution: | Center for Applied Statistics, School of Statistics, Renmin University of China, Beijing 100872, P. R. China;Center for Applied Statistics, School of Statistics, Renmin University of China, Beijing 100872, P. R. China; School of Statistics, University of International Business and Economics, Beijing 100029, P. R. China;Center for Applied Statistics, School of Statistics, Renmin University of China, Beijing 100872, P. R. China; School of Statistics, Beijing Normal University, Beijing 100875, P. R. China; Center for Applied Statistics, School of Statistics, Renmin University of China, Beijing 100872, P. R. China; Department of Medical Engineering and Technology, Xinjiang Medical University, Xinjiang 830011, P. R. China; School of Statistics and Information, Xinjiang University of Finance and Economics, Xinjiang 830012, P. R. China |
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| Abstract: | The lack of covariate data is one of the hotspots of modern statistical analysis. It often appears in surveys or interviews, and becomes more complex in the presence of heavy tailed, skewed, and heteroscedastic data. In this sense, a robust quantile regression method is more concerned. This paper presents an inverse weighted quantile regression method to explore the relationship between response and covariates. This method has several advantages over the naive estimator. On the one hand, it uses all available data and the missing covariates are allowed to be heavily correlated with the response; on the other hand, the estimator is uniform and asymptotically normal at all quantile levels. The effectiveness of this method is verified by simulation. Finally, in order to illustrate the effectiveness of this method, we extend it to the more general case, multivariate case and nonparametric case. |
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| Keywords: | Robust quantile regression missing covariates selection probability Kernel estimator weighting method |
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