  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.
