Estimation in a Cox regression model with a change-point according to a threshold in a covariate. (English) Zbl 1040.62090

Pons, Odile

Ann. Stat. 31, No. 2, 442-463 (2003).

Summary: 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 estimators 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.

MSC:

62N02	Estimation in survival analysis and censored data
62E20	Asymptotic distribution theory in statistics
62F12	Asymptotic properties of parametric estimators
62G05	Nonparametric estimation
62M09	Non-Markovian processes: estimation
60F05	Central limit and other weak theorems

Keywords:

hazard function; right censoring

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