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Smooth and non-smooth estimates of a monotone hazard

Piet Groeneboom and Geurt Jongbloed

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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.

Chapter information

Banerjee, M., Bunea, F., Huang, J., Koltchinskii, V., and Maathuis, M. H., eds., From Probability to Statistics and Back: High-Dimensional Models and Processes -- A Festschrift in Honor of Jon A. Wellner, (Beachwood, Ohio, USA: Institute of Mathematical Statistics, 2013) , 174-196

First available in Project Euclid: 8 March 2013

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62G05: Estimation 62G05: Estimation
Secondary: 62E20: Asymptotic distribution theory

failure rate isotonic regression asymptotics penalized estimators smoothing spiking behavior

Copyright © 2010, Institute of Mathematical Statistics


Groeneboom, Piet; Jongbloed, Geurt. Smooth and non-smooth estimates of a monotone hazard. From Probability to Statistics and Back: High-Dimensional Models and Processes -- A Festschrift in Honor of Jon A. Wellner, 174--196, Institute of Mathematical Statistics, Beachwood, Ohio, USA, 2013. doi:10.1214/12-IMSCOLL913.

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