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 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 language | English |
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Pages (from-to) | 43-67 |
Number of pages | 25 |
Journal | Journal of Statistical Planning and Inference |
Volume | 191 |
DOIs | |
Publication status | Published - 2017 |
Keywords
- Asymptotic normality
- Cox regression model
- Hazard rate
- Isotonic estimation
- Isotonized smoothed Breslow estimator
- Kernel smoothing
- Maximum smoothed likelihood estimator