Model Checking For Parameter Quantile Regression Model With Right-censored Response Variable

The parametric model has the good properties of good explanation,easy to understand and accurate prediction.In the existing literature,the mean regression for parametric models has attracted many scholars' attention.Compared with mean regression models,quantile regression models can not only reflect the information of response variables in mean value,but also reflec-t the information of response variables in other quantiles,so this paper focuses on parameter quantile regression models.In many practical applications,the real data structure is often very complex,for example,due to the test termination,imperfection of measurement equipment and conditions,the data will often be censored.This paper mainly studies the model checking prob-lem of the parameter quantile regression model when the response variable is right censored.It is noted that the existing methods will fail when the covariate dimension is high,so it is mean-ingful to focus on the parameter quantile regression model with high dimensional covariates and right censored response variableFor the model checking problem of the parameter quantile regression model with the re-sponse variable right censored,we first use product limit estimation to tackle the right censored data.Then using the integral method proposed in the classical model checking literature,we construct a test statistic based on the mapping of a residual empirical process.The test method is not only applicable to the case where the dimension of the covariate is high,but also avoids the selection of kernel function and related band width.Furthermore,we consider the large sample properties of the proposed test method under the null hypothesis,and the asymptotic limit is proved under the null hypothesis.Consequently,a corresponding test statistic is con-structed.Due to the complexity of its asymptotic distribution,wild bootstrap method is resorted to obtain the test critical value approximately.Finally,numerical simulation is used to verify the effectiveness of the proposed test method under various settings with different dimensions of covariates.The simulation results show that under the null hypothesis the sizes of the pro-posed test method are close to the nominal level in the low-dimensional and high-dimensional covariate cases.While under the alternative hypothesis,with the model farther away from the null model,the power of the test tend to be 1.This shows that the proposed method in this paper is effective when processing high-dimensional data.