Local Linear Estimator Of Multivariate Conditional Quantile With Censoring Indicator In Missing At Random

It is well known that there are some very good features when using conditional quantiles to fit data.For example,when encountering heavy-tailed data or diverging data,the conditional quantiles are very robust,especially the conditional median.Therefore,the study of conditional quantiles has always been a hot issue in mathematical statistics.In the past,the study of conditional quantiles was often carried out under complete data,but in real life,the data we encounter is often not complete data.Censored data is a type of data that we often encounter in practical applications.Censored data is divided into two types: censored indicators missing at random,and censored indicators missing completely at random.Censored indicators amissing at random is the more general case.In the past when a large number of censored indicators are missing at random,the common method is to delete all the data that censored indicators are missing at random.For the remaining right censored data that can observe the censored indicators,the traditional method is used for statistical inference.In this paper,we construct a weighted local linear calibration estimator,an imputation estimator and an inverse probability estimator of multivariate conditional distribution function with censoring indicators missing at random,respectively.Furthermore,the corresponding estimators of multivariate conditional quantiles are derived by using these estimators,and the asymptotic normality results of these estimators are established,which extends the results of Yu and Jones(1998)from complete data to right-censored data with the censoring indicators missing at random and multidimensional covariates.Finally,the simulation studies are conducted to illustrate the finite sample performance of the estimators.