Hazard function given a functional variable:: Non-parametric estimation under strong mixing conditions

We study here the kernel type, non-parametric estimation of the conditional hazard function, based on a sample of functional dependent data. The almost complete convergence of the conditional hazard estimate is easily derived using the properties referred by Ferraty et al for the conditional distribution and conditional density estimates. The asymptotic bias and variances of the three estimates (conditional density, distribution and hazard) are calculated and compared with the results obtained in p-dimensional non-parametric kernel estimation. The asymptotic normality is established for the three mentioned estimates. Finally, an application to an earthquake data set is made.