THE ESTIMATION OF THE CONDITIONAL HAZARD FUNCTION WITH A RECURSIVE KERNEL FORM CENSORED FUNCTIONAL ERGODIC DATA .

In this paper, we propose a non-parametric estimator of the conditional hazard function weighted on the recursive kernel method in the context of functional stationary ergodic process with the explanatory variable taking values in a semi-metric space and a censored response. The conditional hazard rate plays an important role in the statistcis, it arise in a variety of fields inculding econometrics, epidemiology environmental science and many others. We consider the case of functional ergodic data because it has been an increasing interest in this area in recent year. This ergodic hypothesis is a fundamental axiom of statistical physics in order to examine the thermodynamic properties of gases, atoms, electrons or plasmas , also makes it possible to avoid complicated probabilistic calculations of the mixing condition. We consider a recursive estimate when the observations are strictly stationary ergodic data, it should be noted that the advantage of the recursive estimate is that the smoothing parameter is linked to the observation (Xi,Yi), wich permits to update our estimator for each additional observation. Under hypothesis, we establish the almost surely convergence of the proposed estimator.