Estimation Of Regression Function And Conditional Quantile With Censoring Indicators Missing At Random

Conditional quantiles are widely used in financial analysis,medical disease research and other fields.In the actual survey data,there are inevitably some divorced samples and heavy tailed data.At this time,the use of conditional quantiles can also maintain good robustness.In the traditional parameter estimation,the probability distribution of the data needs to be assumed first,In order to further estimate the parameters,but in the face of complex situation,it is a very difficult problem to find a suitable density function.This kind of defect can be solved well by using kernel estimation method.Its essence starts from the connection between data itself,and it is not necessary to know the distribution of data.Censored data has always been the focus of research in mathematical statistics.In practical applications,there are often cases that the investigation records are not standardized or involve the privacy of the respondents,resulting in a great discount in the integrity of the sample set.In the right censored model,the censored index (90)7)(6is often used to distinguish such data.Many scholars have found that some missing behaviors exist in deleted indicators due to special reasons when analyzing complex data such as disease transmission.Therefore,it is of great practical significance to study MAR(censoring indicators missing at random)In this paper,we construct estimators of a nonparametric functions and conditional quantiles and establish the asymptotic normality when the data are right censored and the censoring indicators are missing at random.First,we construct the calibration weighted kernel estimator,the interpolation weighted kernel estimator and the inverse probability weighted kernel estimator for the conditional distribution function.Then,the kernel estimators of conditional quantiles are derived from these three estimators,and their asymptotic normality is established.Secondly,we construct the interpolation weighted local polynomial estimators and calibration weighted local polynomial estimators of a nonparametric function.Then,the interpolating weighted local polynomial estimators and the calibrated weighted local polynomial estimators of conditional density,conditional distribution and conditional quantile function are derived,and the asymptotic normality of these estimators is established and proved.Finally,the simulation studies are conducted to illustrate the finite sample performance of the estimators,and the advantages and disadvantages of each estimation method are analyzed.