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

2016/11/04 by Hendrik P. Lopuhaä, Lopuhaä, Hendrik P., Eni Musta +1
Mathematics · #FOS: Mathematics #Statistics Theory (math.ST) #math.ST #stat.TH

paper · pdf · doi:10.48550/arxiv.1611.01506

arXiv admin note: text overlap with arXiv:1609.06617

arxiv created 2018/05/17 · arxiv updated 2018/05/18

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≥ 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.

Citations

• Smoothed isotonic estimators of a monotone baseline hazard in the Cox model

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