Smoothed isotonic estimators of a monotone baseline hazard in the Cox model

TL;DR

This paper investigates smoothed estimators for a monotone baseline hazard in the Cox model, analyzing their asymptotic properties and demonstrating their equivalence and practical performance through numerical results.

Contribution

It provides a theoretical analysis of the asymptotic normality and equivalence of two smoothed estimators for the baseline hazard in the Cox model.

Findings

Both estimators are asymptotically normal at rate n^{m/(2m+1)}.

The estimators are asymptotically equivalent.

Numerical results show similar performance in confidence interval estimation.

Abstract

We consider the smoothed maximum likelihood estimator and the smoothed Grenander-type estimator for a monotone baseline hazard rate $\lambda_0$ in the Cox model. We analyze their asymptotic behavior and show that they are asymptotically normal at rate $n^{m/(2m+1)}$, when~$\lambda_0$ is $m\geq 2$ times continuously differentiable, and that both estimators are asymptotically equivalent. Finally, we present numerical results on pointwise confidence intervals that illustrate the comparable behavior of the two methods.