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arXiv · 1611.01506

Isotonized smooth estimators of a monotone baseline hazard in the Cox model

Hendrik P. Lopuhaä·Eni Musta
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Abstract

We consider two isotonic smooth estimators for a monotone baseline hazard in the Cox model, a maximum smooth likelihood estimator and a Grenander-type estimator based on the smoothed Breslow estimator for the cumulative baseline hazard. We show that they are both asymptotically normal at rate $n^{m/(2m+1)}$, where $m\geq 2$ denotes the level of smoothness considered, and we relate their limit behavior to kernel smoothed isotonic estimators studied in Lopuhaä and Musta (2016). It turns out that the Grenander-type estimator is asymptotically equivalent to the kernel smoothed isotonic estimators, while the maximum smoothed likelihood estimator exhibits the same asymptotic variance but a different bias. Finally, we present numerical results on pointwise confidence intervals that illustrate the comparable behavior of the two methods.

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Hendrik P. Lopuhaä, Eni Musta. 2018-05-17. Isotonized smooth estimators of a monotone baseline hazard in the Cox model. https://arxiv.org/abs/1611.01506

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