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

Abstract

We consider the Cox regression model and study the asymptotic global behavior of the Grenandertype estimator for a monotone baseline hazard function. This model is not included in the general setting of [8]. 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.