We consider the problem of nonparametric estimation of the conditional hazard function for functional mixing data. More precisely, given a strictly stationary random variables Z i = (X i , Y i ) i∈N , we investigate a kernel estimate of the conditional hazard function of univariate response variable Y i given the functional variable X i . The principal aim of this paper is to give the mean squared convergence rate and to prove the asymptotic normality of the proposed estimator.
We propose a new nonparametric estimator of the conditional hazard function. To this end we define nonparametric estimators of the conditional cumulative distribution and the density functions of a scalar response variable Y given a functional random variable X. The conditional cumulative distribution, density and hazard functions for independent functional data are estimated nonparametrically. Our estimates are based on a recursive approach. We establish under appropriate conditions the almost sure and the quadratic average convergence rates of the resulting hazard rate estimator. Furthermore, a simulation study and an application to a real dataset illustrate our methodology.
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