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A general quantile residual life model for length‐biased right‐censored data
Author(s) -
Bai Fangfang,
Chen Xuerong,
Chen Yan,
Huang Tao
Publication year - 2019
Publication title -
scandinavian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.359
H-Index - 65
eISSN - 1467-9469
pISSN - 0303-6898
DOI - 10.1111/sjos.12390
Subject(s) - quantile , mathematics , residual , estimator , censoring (clinical trials) , outlier , statistics , asymptotic distribution , consistency (knowledge bases) , resampling , covariance , estimating equations , quantile regression , quantile function , econometrics , probability distribution , algorithm , moment generating function , geometry
Abstract The quantile residual lifetime function provides comprehensive quantitative measures for residual life, especially when the distribution of the latter is skewed or heavy‐tailed and/or when the data contain outliers. In this paper, we propose a general class of semiparametric quantile residual life models for length‐biased right‐censored data. We use the inverse probability weighted method to correct the bias due to length‐biased sampling and informative censoring. Two estimating equations corresponding to the quantile regressions are constructed in two separate steps to obtain an efficient estimator. Consistency and asymptotic normality of the estimator are established. The main difficulty in implementing our proposed method is that the estimating equations associated with the quantiles are nondifferentiable, and we apply the majorize–minimize algorithm and estimate the asymptotic covariance using an efficient resampling method. We use simulation studies to evaluate the proposed method and illustrate its application by a real‐data example.