Asymptotic Properties Of Wavelet Estimation In Heteroscedaticity Model With Censoring Indicators Missing At Random

Survival analysis is a statistical method to study survival phenomena and response time data and their rules.The analysis of death time in biological statistics is one of the earliest and most in-depth research direction in this field.In recent years,the missing data regression model of survival time has been widely studied and applied,and many scholars have proposed many estimation methods.When the response variable(4 is censored by the censoring variable,the observed variable is(5=min(?4,?,and the censoring indicator is denoted as=(?4??.In the missing data,the censoring indicator conveys the information whether the observation time is the survival time researchers needed or the missing time.If this information is incomplete,the censoring indicators will be missing.When the censoring indicatoris not fully observed,is the indicative function of whetheris fully observed.As a popular new method in statistical analysis in recent years,wavelet estimation re-quires less smoothness of nonparametric functions than other methods such as kernel estima-tion,which has good time-frequency localization characteristics,and the obtained large sam-ple properties are more ideal.This paper considers heteroscedastic regression model(4₄)=2)(₄))+₄)0)₄),1?4)?9),where²₄)=1)(₄)),here(₄),₄))being fixed design points,2)?·?and1)?·?being unknown functions defined on[0,1],0)₄)being independent random errors with mean zero.Assuming that(4₄)are right censored randomly and the censoring distribution function is known or unknown,this paper mainly discusses the case of censoring indicators missing at ran-dom,the calibration,interpolation and inverse probability wavelet estimation of2)?·?and1)?·?in the heteroscedastic model are constructed respectively under the condition of known and unknown censoring distribution,on this basis,the asymptotic properties of wavelet estimation2)?·?under these two conditions are proposed,and their asymptotic normality of interpolation wavelet estimation is proved under certain conditions.Finally,we extend the results of the asymptotic normality to the case where the model variances are the same.