右删失长度偏差数据分位数差的非参数估计

Nonparametric Estimation of the Quantile Differences for Right-censored and Length-biased Data

利用长度偏差数据所特有的辅助信息,对带右删失的长度偏差数据的分位数差提出了一种新的非参数估计.该方法提高了估计的有效性,所得的估计量形式简洁,便于计算.同时,本文用经验过程理论建立了该分位数差估计的相合性及渐近正态性,并给出方差估计的重抽样方法.本文还通过数值模拟考察了该估计量在有限样本下的表现,并将其应用到一个关于老年痴呆的实际数据中.

We propose a novel nonparametric estimator of the quantile difference based on the length-biased data subject to potential right censoring.In order to improve efficiency,the new estimator incorporates the auxiliary information inherent in the prevalent sampling design.And it has a simple expression,which is easy to compute.Moreover,the consistency and asymptotic normality of this quantile difference estimator are established using the empirical process theory and the asymptotic variance can be obtained consistently via a resampling method.We also demonstrate that the proposed estimator exhibits satisfactory performance with finite sample size through the Monte-Carlo studies and an analysis of a real data example about the Alzheimer’s disease.