In this paper we investigate the asymptotic mean square error and the rates of convergence of the estimator based on the local linear method of the conditional hazard function. Under some general conditions, the expressions of the bias and variance are given. The efficiency of our estimator is evaluated through a simulation study. We proved, theoretically and on the scope of a simulation study, that our proposed estimator has better performance than the estimator based on the standard kernel method.

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We study the nonparametric local linear estimation of the conditional hazard function of a scalar response variable given a functional explanatory variable, when the functional data are α-mixing dependency and we give the uniform almost complete convergence with rates of this function.