Results on standard estimators in the Cox model

Abstract

We consider the Cox regression model and prove some properties of the maximum partial likelihood estimator ${\hat{\beta }}_n$ and of the the Breslow estimator ${\Lambda }_n$. The asymptotic properties of these estimators have been widely studied in the literature but we are not aware of a reference where it is shown that they have uniformly bounded moments. These results are needed, for example, when studying global errors of shape restricted estimators of the baseline hazard function.