The Cox partial likelihood and Breslow estimators have bounded moments of any order on high-probability events, under exponential moment conditions on the covariates.
On the $L_p$-error of the Grenander-type estimator in the Cox model
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abstract
We consider the Cox regression model and study the asymptotic global behavior of the Grenander-type estimator for a monotone baseline hazard function. This model is not included in the general setting of Durot (2007). However, we show that a similar central limit theorem holds for $L_p$-error of the Grenander-type estimator. We also propose a test procedure for a Weibull baseline distribution, based on the $L_p$-distance between the Grenander estimator and a parametric estimator of the baseline hazard. Simulation studies are performed to investigate the performance of this test.
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Results on standard estimators in the Cox model
The Cox partial likelihood and Breslow estimators have bounded moments of any order on high-probability events, under exponential moment conditions on the covariates.