Nonparametric estimation of the maximum hazard under dependence conditions

The maximum of a hazard function is a parameter of great importance in seismicity studies, because it constitutes the maximum risk of occurrence of an earthquake in a given interval of time. By means of kernel nonparametric estimates of the first derivative of the hazard function, we establish uniform convergence properties and asymptotic normality of an estimate of the maximum, in a context of strong mixing dependence. A small simulation study and a practical example show the performance of the proposed estimator in finite samples.