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 nm∕(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.

Original languageEnglish
Pages (from-to)43-67
Number of pages25
JournalJournal of Statistical Planning and Inference
Volume191
DOIs
Publication statusPublished - 2017

    Research areas

  • Asymptotic normality, Cox regression model, Hazard rate, Isotonic estimation, Isotonized smoothed Breslow estimator, Kernel smoothing, Maximum smoothed likelihood estimator

ID: 28356128