Theoretical and practical aspects of the quadratic error in the local linear estimation of the conditional density for functional data

The problem of the nonparametric local linear estimation of the conditional density of a scalar response variable given a random variable taking values in a semi-metric space is considered. Some theoretical and practical asymptotic properties of this estimator are established. The usefulness of the estimator is highlighted through the exact expression involved in the leading terms of the quadratic error, and by conducting a computational investigation to show the superiority of this estimation method for the conditional density and then for the conditional mode. Moreover, in order to verify the pertinence of the technique, from a practical point of view, it is applied to a real dataset.