An Asymptotic Linear Representation for the Breslow Estimator

TL;DR

This paper derives an asymptotic linear representation for the Breslow estimator in the Cox model, facilitating understanding of its statistical properties and potential applications in survival analysis.

Contribution

It introduces a novel asymptotic linear representation of the Breslow estimator involving an average of independent variables and a correction term.

Findings

Representation has a remainder term close to 1/n

Provides a basis for asymptotic inference in Cox models

Enhances understanding of the estimator's behavior

Abstract

We provide an asymptotic linear representation for the Breslow estimator of the baseline cumulative hazard function in the Cox model. Our representation consists of an average of independent random variables and a term involving the difference between the maximum partial likelihood estimator and the underlying regression parameter. The order of the remainder term is arbitrarily close to 1/n.