Nonparametric estimation of the maximum of conditional hazard function under dependence conditions for functional data

Abstract

The maximum of the conditional hazard function is a parameter of great importance in statistics, in particular in seismicity studies, because it constitutes the maximum risk of occurrence of an earthquake in a given interval of time. Using the kernel nonparametric estimates based on convolution kernel techniques of the rst derivative of the conditional hazard function, we establish the asymptotic behavior of a hazard rate in the presence of a functional explanatory variable and asymptotic normality of the maximum value in the case of a strong mixing process.

Keywords: Almost complete convergence; Asymptotic normality; Conditional hazard function; Functional data; Nonparametric estimation; Small ball probability; Strong mixing processes