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VOL. 9 | 2013 Smooth and non-smooth estimates of a monotone hazard
Piet Groeneboom, Geurt Jongbloed

Editor(s) M. Banerjee, F. Bunea, J. Huang, V. Koltchinskii, M. H. Maathuis

## Abstract

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 [ Statist. Sinica 3 (1993) 501–515; Ann. Statist. 27 (1999) 338–360]. 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.

## Information

Published: 1 January 2013
First available in Project Euclid: 8 March 2013

zbMATH: 1325.62074
MathSciNet: MR3202633

Digital Object Identifier: 10.1214/12-IMSCOLL913

Subjects:
Primary: 62G05 , 62G05
Secondary: 62E20

Keywords: asymptotics , failure rate , isotonic regression , penalized estimators , smoothing , spiking behavior