Efficient estimation for the proportional hazards model with interval censoring

• 成果类型: Article
• 署名作者: Huang, J
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• 发表日期: 1996
• 页码: 540-568
• 关键词: FAILURE TIME DATA; maximum-likelihood; statistical-analysis; regression; Consistency

摘要

The maximum likelihood estimator (MLE) for the proportional hazards model with case 1 interval censored data is studied. It is shown that the MLE for the regression parameter is asymptotically normal with root n convergence rate and achieves the information bound, even though the MLE for the baseline cumulative hazard function only converges at n(1/3) rate. Estimation of the asymptotic variance matrix for the MLE of the regression parameter is also considered. To prove our main results, we also establish a general theorem showing that the MLE of the finite-dimensional parameter in a class of semiparametric models is asymptotically efficient even though the MLE of the infinite-dimensional parameter converges at a rate slower than root n. The results are illustrated by applying them to a data set from a tumorigenicity study.