## The Annals of Statistics

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

Odile Pons

#### Abstract

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.

#### Article information

Source
Ann. Statist., Volume 31, Number 2 (2003), 442-463.

Dates
First available in Project Euclid: 22 April 2003

https://projecteuclid.org/euclid.aos/1051027876

Digital Object Identifier
doi:10.1214/aos/1051027876

Mathematical Reviews number (MathSciNet)
MR1983537

Zentralblatt MATH identifier
1040.62090

Subjects
Primary: 62F12: Asymptotic properties of estimators 62G05: Estimation 60M09

#### Citation

Pons, Odile. Estimation in a Cox regression model with a change-point according to a threshold in a covariate. Ann. Statist. 31 (2003), no. 2, 442--463. doi:10.1214/aos/1051027876. https://projecteuclid.org/euclid.aos/1051027876

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