Smooth and non-smooth estimates of a monotone hazard

Details Smooth and non-smooth estimates of a monotone hazard Smooth and non-smooth estimates of a monotone hazard

2011-02-19

arxiv.org/abs/1102.3999v1

Mathematics

Statistics Theory

19 pages, 7 figures, submitted to the volume in the IMS Lecture Notes Monograph Series in honor of the 65th birthday of Jon We

Scientific paper

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.

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