Smoothed Isotonic Estimators of a Monotone Baseline Hazard in the Cox Model

Hendrik P. Lopuhaä; Eni Musta

doi:10.1111/sjos.12321

Smoothed Isotonic Estimators of a Monotone Baseline Hazard in the Cox Model

Hendrik P. Lopuhaä, Eni Musta

Statistics

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Abstract

We consider the smoothed maximum likelihood estimator and the smoothed Grenander-type estimator for a monotone baseline hazard rate 0 in the Cox model. We analyze their asymptotic behaviour and show that they are asymptotically normal at rate nm=.2mC1/, when 0 is m 2 times continuously differentiable, and that both estimators are asymptotically equivalent. Finally, we present numerical results on pointwise confidence intervals that illustrate the comparable behaviour of the two methods.

Original language	English
Pages (from-to)	753-791
Number of pages	39
Journal	Scandinavian Journal of Statistics: theory and applications
Volume	45
DOIs	https://doi.org/10.1111/sjos.12321
Publication status	Published - 2018

Keywords

asymptotic normality
Cox regression model
hazard rate
isotonic estimation
kernel smoothing
smoothed Grenander estimator
smoothed maximum likelihood estimator

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10.1111/sjos.12321

46605061 - Lopuha-_et_al-2018-Scandinavian_Journal_of_StatisticsFinal published version, 597 KBLicence: CC BY

Cite this

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AB - We consider the smoothed maximum likelihood estimator and the smoothed Grenander-type estimator for a monotone baseline hazard rate 0 in the Cox model. We analyze their asymptotic behaviour and show that they are asymptotically normal at rate nm=.2mC1/, when 0 is m 2 times continuously differentiable, and that both estimators are asymptotically equivalent. Finally, we present numerical results on pointwise confidence intervals that illustrate the comparable behaviour of the two methods.

KW - asymptotic normality

KW - Cox regression model

KW - hazard rate

KW - isotonic estimation

KW - kernel smoothing

KW - smoothed Grenander estimator

KW - smoothed maximum likelihood estimator

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JF - Scandinavian Journal of Statistics: theory and applications

ER -

Smoothed Isotonic Estimators of a Monotone Baseline Hazard in the Cox Model

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Keywords

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