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Asymptotic normality of the nonparametric conditional density function estimate with functional variables for quasi-associated data

Hamza Daoudi, Boubaker Mechab, Samir Benaissa, Abbes Rabhi

Abstract



The main goal of this paper is to study the asymptotic normality of the estimate of the conditional density function of a scalar response variable Y given a hilbertian random variable X in the quasi-associated framework. Our approach is based on the Doob's technique. It is shown that, under the concentration property on small balls of the probability measure of the functional estimator and some regularity conditions, the kernel estimate of the conditional density fuction are asymptotically normally distributed.

Keywords


Asymptotic normality, conditional density function, quasi-association, nonparameter kernel estimation.

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