Nonparametric estimation of hazard rate under the constraint of monotonicity

This article shows how to smoothly "monotonize" standard kernel estimators of hazard rate, using bootstrap weights. Our method takes a variety of form s, depending on choice of kernel estimator and on the distance function use d to define a certain constrained optimization problem. We confine attentio n to a particularly simple kernel approach and explore a range of distance functions. It is straightforward to reduce "quadratic" inequality constrain ts to "linear" equality constraints, and so our method may be implemented u sing little more than conventional Newton-Raphson iteration. Thus, the nece ssary computational techniques are very familiar to statisticians. We show both numerically and theoretically that monotonicity, in either direction, can generally be imposed on a kernel hazard rate estimator regardless of th e monotonicity or otherwise of the true hazard rate. The case of censored d ata is easily accommodated. Our methods have straightforward extension to t he problem of testing for monotonicity of hazard rate, where the distance f unction plays the role of a test statistic.