Composite Quantile Estimation For Partially Linear Varying Coefficient Models With Missing Dat

Data missing is inevitable in real life and work.The missing probability and missing mechanism of data will affect the estimation accuracy of analysis method and even draw wrong conclusions.The effective processing of missing data depends on robust estimation methods and appropriate models,there are certain limitations in the general linear model due to strong assumptions.In order to improve the interpretability and flexibility of the model further,some scholars have proposed partially linear varying coefficient model.In this paper,based on the composite quantile regression method,we study the parameter and function estimation and variable selection of partially linear varying coefficient model with response and partial covariables missing at random.Specifically,the research contents include:(1)We propose a robust estimation method in the partially linear varying coefficient model when response and partial covariables are missing at random.Based on B-spline approximations and probability-weighting method,we propose a weighted Bspline composite quantile regression method to estimate the nonparametric function and the regression coefficients.Meanwhile,the asymptotic property of the obtained estimates is proved under certain conditions.Finally,a numerical simulation study is carried out.(2)We propose a variable selection method in the partially linear varying coefficient model when response and partial covariables are missing at random.The adaptive LASSO penalty function combined with B-spline approximations,inverse probabilityweighting and composite quantile regression method was used to select the variables of the parameter components in the model.Then,under some regular conditions,the oracle property of the proposed variable selection method is studied.Finally,simulation studies are presented to illustrate the behavior of the proposed method.(3)The proposed method is applied to the analysis of Boston housing price data,and the effectiveness of the proposed method is considered from the perspective of prediction.The average absolute prediction error(MAPE)is used as the standard to measure the prediction effect.The analysis results show that the proposed method is effective.