Statistical Inference For The Weighted Composite Quantile Regression Model With Nonignorable Missing Data

In statistical research,missing data is ubiquitous,especially statistical inference of nonignorable missing data is very difficult.Modeling of nonignorable missing data is mainly based on traditional linear regression model,which needs to assume that the error terms are independent of the same distribution.In real life,the assumptions are difficult to satisfy.When the data has thick tail errors,outliers,etc.,the traditional linear regression model will no longer be applicable.Compared with the traditional linear regression,the quantile regression is more relaxed.It is based on the distribution of different quantile points of the response variable,which can more accurately describe the influence of the independent variable on the variation range of the response variable and the shape of the conditional distribution,so it is robust.Further on the basis of quantile regression,the composite quantile regression preserves the robustness of the quantile regression and improves the efficiency of the estimation through a composite approach.For the nonignorable missing data in this paper,it assumes that the response probability model obeys the parameterized logistic distribution,according to the established composite quantile regression model,the inverse probability weighted composite quantile regression estimation form of the parameters is derived.The parameter estimation is obtained by the maximum likelihood method,the semiparametric likelihood method and the empirical likelihood method.The inverse probability weighted composite quantile regression method based on likelihood estimation is simple,and the estimation efficiency of the regression coefficient is higher than the inverse probability weighted least squares method.By analyzing the simulation experiment and the actual data application,it is concluded that the estimation method is superior to the inverse probability weighted least squares coefficient estimate in most cases.