On inconsistency of Breslow's estimator as an estimator of the hazard rate in the Cox model.

In the Cox proportional hazards model, Breslow's estimator of the cumulative hazard function is well known. This estimator is sometimes presented in such a way that it appears to offer a method of estimating the hazard rate function as well. We state and prove an asymptotic result for this estimator of the hazard rate, which shows that the estimator is inconsistent, and that it is asymptotically unbiased.