Estimating Equation Estimators Of Quantile Differences Base On Length-Biased And Right-Censored Data

Quantile difference is a commonly used numerical feature of random variables,which is widely used in practical problems such as survival analysis,economics,and sociology.It is usually used to describe the degree of dispersion of random variables,and is insensitive to heavy-tailed distributions and extreme values.Existing research on quantile difference mostly focuses on the fields of right-censored data,left-truncated and right-censored data,but the quantile difference of length-biased and right-censored data is also worthy of our study.In this paper,firstly,we combine the idea of redistributing weights to construct a nonsmooth inverse probability weight estimating equation to estimate the quantile difference.In order to further improve the efficiency of the estimators,we use the kernel smoothing method to process the inverse probability weight estimating equation,and obtains smooth estimating equation.In addition,in order to make full use of the auxiliary information contained in the data for the data characteristics of the length-biased and right-censored data,the article uses AIPWCC(Augmented Inverse Probability Weighted Complete-Case)to construct the estimating equation.Then the consistency and asymptotic normality of these estimators was established.And numerical simulations are used to verify the performance of these estimators in a limited sample.The results show that in the sense of lower mean square error,the smooth estimating equation is more effective than the other two estimators.In the sense of lower the asymptotic variance,the AIPWCC estimating equation is more effective than the other two estimators.