Results on standard estimators in the Cox model

TL;DR

This paper investigates the properties of key estimators in the Cox regression model, focusing on their asymptotic behavior and the boundedness of their moments, which are crucial for understanding their global error characteristics.

Contribution

It provides new theoretical results demonstrating that the maximum partial likelihood estimator and Breslow estimator have uniformly bounded moments, filling a gap in existing literature.

Findings

Proves uniform boundedness of moments for the estimators

Enhances understanding of asymptotic properties in Cox models

Supports analysis of shape-restricted estimators' errors

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.