Regression M-estimators with doubly censored data

• 成果类型: Article
• 署名作者: Ren, JJ; Gu, MG
• 署名单位: Tulane University; McGill University
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/aos/1030741089
• 发表日期: 1997
• 页码: 2638-2664
• 关键词: MAXIMUM-LIKELIHOOD ESTIMATORS; product-limit estimator; linear-regression; survival function; WEAK-CONVERGENCE; self-consistent; large sample; nonparametric estimator; synthetic data

摘要

The M-estimators are proposed for the linear regression model with random design when the response observations are doubly censored. The proposed estimators are constructed as some functional of a Campbell-type estimator (F) over cap(n) for a bivariate distribution function based on data which are doubly censored in one coordinate. We establish strong uniform consistency and asymptotic normality of (F) over cap(n) and derive the asymptotic normality of the proposed regression M-estimators through verifying their Hadamard differentiability property. As corollaries, we show that our results on the proposed M-estimators also apply to other types of data such as uncensored observations, bivariate observations under univariate right censoring, bivariate right-censored observations, and so on. Computation of the proposed regression M-estimators is discussed and the method is applied to a doubly censored data set, which was encountered in a recent study on the age-dependent growth rate of primary breast cancer.