  We consider kernel smoothed Grenander-type estimators for a monotone hazard
rate and a monotone density in the presence of randomly right censored data. We
show that they converge at rate $n^{2/5}$ and that the limit distribution at a
fixed point is Gaussian with explicitly given mean and variance. It is
well-known that standard kernel smoothing leads to inconsistency problems at
the boundary points. It turns out that, also by using a boundary correction, we
can only establish uniform consistency on intervals that stay away from the end
point of the support (though we can go arbitrarily close to the right
boundary).
