  We discuss a number of estimates of the hazard under the assumption that the
hazard is monotone on an interval [0,a]. The usual isotonic least squares
estimators of the hazard are inconsistent at the boundary points 0 and a. We
use penalization to obtain uniformly consistent estimators. Moreover, we
determine the optimal penalization constants, extending related work in this
direction by Woodroofe and Sun (1993) and Woodroofe and Sun (1999). Two methods
of obtaining smooth monotone estimates based on a non-smooth monotone estimator
are discussed. One is based on kernel smoothing, the other on penalization.
