Estimation in a Cox regression model with a change-point according to a threshold in a covariate

• 成果类型: Article
• 署名作者: Pons, O
• 署名单位: Universite Paris Saclay; INRAE; Universite Paris Cite
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/aos/1051027876
• 发表日期: 2003
• 页码: 442-463
• 关键词: hazard rate models; asymptotic-distribution; large sample; likelihood; parameter; tests

摘要

We consider a nonregular Cox model for independent and identically distributed right censored survival times, with a change-point according to the unknown threshold of a covariate. The maximum partial likelihood estimators of the parameters and the estimator of the baseline cumulative hazard are studied. We prove that the estimator of the change-point is n-consistent and the estimator of the regression parameters are n(1/2)-consistent, and we establish the asymptotic distributions of the estimators. The estimators of the regression parameters and of the baseline cumulative hazard are adaptive in the sense that they do not depend on the knowledge of the change-point.