On the $L_p$-error of the Grenander-type estimator in the Cox model

TL;DR

This paper analyzes the asymptotic behavior of a Grenander-type estimator for a monotone baseline hazard in the Cox model, extending existing theory and proposing a new test for Weibull baseline distribution.

Contribution

It extends the CLT for the $L_p$-error of the Grenander estimator to the Cox model and introduces a new test for Weibull baseline hazard.

Findings

Central limit theorem holds for $L_p$-error in Cox model

Proposed test effectively distinguishes Weibull baseline hazards

Simulation studies demonstrate test performance

Abstract

We consider the Cox regression model and study the asymptotic global behavior of the Grenander-type estimator for a monotone baseline hazard function. This model is not included in the general setting of Durot (2007). However, we show that a similar central limit theorem holds for $L_p$-error of the Grenander-type estimator. We also propose a test procedure for a Weibull baseline distribution, based on the $L_p$-distance between the Grenander estimator and a parametric estimator of the baseline hazard. Simulation studies are performed to investigate the performance of this test.