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On Strong Uniform Consistency of Conditional Hazard Function in the Functional Single-Index Model.

Abbes Rabhi, Naouel Belkhir, Sara Soltani

Abstract



In this paper we deal with nonparametric estimate of the conditional hazard function, when the covariate is functional. Kernel type estimators for the conditional hazard function are introduced of a scalar response variable Y given a Hilbertian random variable X when the observations are linked with a single-index structure. We establish the pointwise almost complete convergence and the uniform almost complete convergence (with the rate) of the kernel estimate of this model in various situations, including censored and non-censored data. The rates of convergence emphasize the crucial role played by the small ball proba-bilities with respect to the distribution of the explanatory functional variable.

Keywords


Censored data, conditional hazard function, functional single-index process, functional variable, nonparametric estimation, small ball probability.

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