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Smooth and non-smooth estimates of a monotone hazard

Piet Groeneboom and Geurt Jongbloed

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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.

Chapter information

Source
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

Dates
First available in Project Euclid: 8 March 2013

Permanent link to this document
https://projecteuclid.org/euclid.imsc/1362751187

Digital Object Identifier
doi:10.1214/12-IMSCOLL913

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

Keywords
failure rate isotonic regression asymptotics penalized estimators smoothing spiking behavior

Rights
Copyright © 2010, Institute of Mathematical Statistics

Citation

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. https://projecteuclid.org/euclid.imsc/1362751187.


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