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

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