Weighted Composite Quantile Regression For Liner Model Withrandomly Truncated Data

Compared with the least squares regression, the application conditions of quantile regressionare more relaxed, and the information revealed by quantile regression is more abundant. So the quantile regression method has been developed rapidly and widely used in recent decades since Koenker and Bassett presented the quantile regression theory in 1978. However, quantile regression analysis is only based on a single quantile, so the information revealed is still very limited, and the efficiency of regression estimation is influenced by the specific value of quantile. In order to further improve the efficiency, theZou Hui and Yuan Ming proposed a more efficient composite quantile regression is more comprehensive and more effective in charactering the relationship between the response variables and covariates. because it takes more conditional quantile function into account.To some extent, the theory and application of quantile regression based on full datas have been studied thoroughly. However, in various application fields, most of the statistical datas have a very prominent feature-be truncated, censord or lost. It is one of the important research topics that how to use the existing datas to more fully exploit the information of the truncated, consored, lost datas in the statistical analysis. A more effective way in regression analysis is to adjust the weights of the existing datas, that is, weighted regression.Inthis paper,we consider the linear model under random truncation data. Based onthe weighted quantile regression method proposed by Weihua Zhou(2011), we propose a weighted composite quantile regression for the random truncated linear model.The asymptotic normality of the regression parameter estimation is established.The simulation results show that the proposed weighted combined quantile regression is more effective than the weighted quantile regression method. Since there is no software package available for our weightedcomposite quantile regression calculation in Rsoftware, we first transform ourweightedcomposite quantile calculation into a linear programming problem in standardized form and then simply call the linear programming linprog function in the MATLAB software to complete our simulation.