Aiming at the problem of non parameter estimation of varying coefficient quantile regression model in the case of random missing response variables, an estimation method combining Bspline and inverse probability weighting is proposed. Missing data is inevitable in statistical work. Firstly, the missing probability of response variable is generated by logistic model. Then, the coefficient function of varying coefficient model is approximated by Bspline. The loss function of inverse probability weighted quantile regression is constructed by using missing probability, and the estimation of unknown coefficient function is obtained. In the simulation study, the estimation is compared with the estimation method using complete data directly. It is found that the quantile regression of variable coefficient model combining Bspline and inverse probability weighting performs well in the case of limited samples in the case of random missing of response variables, and simulation results show that the method is effective. Finally, the research method is applied to the relevant data of Oslo collected by the Norwegian Public Roads Administration, and the relationship between the concentration of nitrogen dioxide in the air and the road traffic flow and wind speed is studied. The reasonable conclusion is drawn, which further proves the rationality of the proposed method.
YE Yao, YUAN De-mei. Quantile Regression of Varying Coefficient Model with Missing Response Variables[J]. Journal of Chongqing Technology and Business University(Natural Science Edition）,2022,39(2):46-52