Quantile Regression With Randomly Missing Data

The truncated and censored data often arises in many research fields,such as clinical study,survival analysis and reliability analysis.The missing data brings great difficulties for statistical analysis and leads to the uncertainty of statistical information.Thus,it is important to research that how to make full use of the missing data to discover all the information of complete data.The results of nonlinear regression model for complete data have been relatively perfect.However,the statistical analysis for missing data still needs further to be developed.In this paper,the statistical inference of nonlinear model is studied for truncated and censored data,respectively.The main contributions are as follows.For the right censored data,the parameter estimate of nonlinear model is studied when the response is randomly censored.Firstly,we propose the weighted quantile estimate by combing inverse-probability-weighting and quantile regression for estimating regression parameter,where the weight is defined by Kaplan-Meier estimate.Secondly,the consistency and asymptotic normality of the proposed estimate are given under the appropriate assumptions.Finally,the finite sample performance of the proposed estimate is presented by numerical simulation.In the simulation,we compare the proposed estimate with quantile estimate under complete data and quantile estimate under censored data.The result shows that results of the proposed estimate are close to the ones for quantile estimate with complete data,and are more effective than quantile estimate results with censored data.When the response is randomly truncated,the weighted quantile regression estimation method is proposed for the nonlinear model,in which the truncated data is processed by weighted method defined by Product-Limit estimate.Further,the quantile regression requires that the quantile of the model error be zero,and the estimation efficiency is related to the selection of the quantile.In order to avoid the above shortcomings,we propose a weighted composite quantile estimate which takes into account the effects of multiple quantiles.The consistency and asymptotic normality of the proposed estimator is derived under appropriate assumptions.Finally,the finite sample performance of the proposed method is demonstrated by numerical simulation.The result shows the weighted quantile estimate is asymptotically unbiased,and the weighted composite quantile estimate is more accurate than the weighted quantile estimate.