Multivariate Hazard Rates under Random Censorship

The data consists of multivariate failure times under right random censorship. By the kernel smoothing technique, convolutions of cumulative multivariate hazard functions suggest estimators of the so-called multivariate hazard functions. We establish strong i.i.d. representations and uniform bounds of the remainder terms on some compact sets of the underlying space. Thus asymptotic normality and uniform consistency on such sets are obtained. The asymptotic mean squared error gives an optimal bandwidth by the plug-in method. Simulations assess the performance of our estimators.