Nonparametric kernel estimation in counting processes with explanatory variables

Abstract

SUMMARY Cox's proportional hazards model assumes that the duration hazard rate factors into a product of a baseline hazard rate and a nonegative function of explanatory variables. An estimate of the baseline hazard rate, hence also of overall hazard rate, is proposed, based on a smoothing procedure using a kernel function. It is shown that the proposed estimator is uniformly consistent and converges weakly to a Gaussian process. Bandwidth selection issues are also discussed.