  We consider two isotonic smooth estimators for a monotone baseline hazard in
the Cox model, a maximum smooth likelihood estimator and a Grenander-type
estimator based on the smoothed Breslow estimator for the cumulative baseline
hazard. We show that they are both asymptotically normal at rate
$n^{m/(2m+1)}$, where $m\geq 2$ denotes the level of smoothness considered, and
we relate their limit behavior to kernel smoothed isotonic estimators studied
in Lopuha\"a and Musta (2016). It turns out that the Grenander-type estimator
is asymptotically equivalent to the kernel smoothed isotonic estimators, while
the maximum smoothed likelihood estimator exhibits the same asymptotic variance
but a different bias. Finally, we present numerical results on pointwise
confidence intervals that illustrate the comparable behavior of the two
methods.
