  We consider the smoothed maximum likelihood estimator and the smoothed
Grenander-type estimator for a monotone baseline hazard rate $\lambda_0$ in the
Cox model. We analyze their asymptotic behavior and show that they are
asymptotically normal at rate $n^{m/(2m+1)}$, when~$\lambda_0$ is $m\geq 2$
times continuously differentiable, and that both estimators are asymptotically
equivalent. Finally, we present numerical results on pointwise confidence
intervals that illustrate the comparable behavior of the two methods.
