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Isotonized smooth estimators of a monotone baseline hazard in the Cox model. (English) Zbl 1376.62052

Summary: 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 [the authors, “Smoothed isotonic estimators of a monotone baseline hazard in the Cox model”, Preprint, arXiv:1609.06617]. 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.

MSC:

62N02 Estimation in survival analysis and censored data
62G05 Nonparametric estimation
62E20 Asymptotic distribution theory in statistics
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