The Horvitz-Thompson Weighting Method for Quantile Regression Estimation in the Presence of Missing Covariates
Received:March 17, 2020  Revised:January 20, 2021
Key Word: Robust quantile regression   Missing covariates   Selection probability   Kernel estimator  Horvitz-Thompson Weighting Method.  
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Author NameAffiliationAddress
Maozai Tian Center for Applied Statistics, School of Statistics, Renmin University of China Center for Applied Statistics, School of Statistics, Renmin University of China
Zhaoji Chu Center for Applied Statistics, School of Statistics, Renmin University of China Center for Applied Statistics, School of Statistics, Renmin University of China
Lingnan Tai Center for Applied Statistics, School of Statistics, Renmin University of China Center for Applied Statistics, School of Statistics, Renmin University of China
Wei Xiong Center for Applied Statistics, School of Statistics, Renmin University of China Center for Applied Statistics, School of Statistics, Renmin University of China
Xu Guo Center for Applied Statistics, School of Statistics, Renmin University of China Center for Applied Statistics, School of Statistics, Renmin University of 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 them. Between reaction and covariate. This method has several advantages over simple estimation. First, it uses all available data to lose information. Second, the missing covariates are allowed to be heavily correlated with the response. Third, the estimator is uniform and asymptotically normal at all quantile levels. In order to illustrate the effectiveness of the method, we extend it to the more general case, multivariate case and nonparametric case. Finally, the effectiveness of the method is verified by simulation.
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