New developments on (non-)normalized continuous associated-kernel density estimators
Résumé
We consider the general modern notion of the so-called associated kernels for smoothing density function on a given support T subset of R. According to the recent and global properties of normalized discrete associated-kernel estimators, we here investigate the continuous associated-kernel contexts in a completely different way. Diverse and numerous in the literature, the standard (non-)normalized density estimators by non-classical kernels have great interests, including modified versions for reducing the possible boundary bias. We first show, under specific assumptions such the asymptotic unimodality on the continuous associated kernel, that the normalizing random variable also converges in mean square to 1. We then deduce the consistency of the considered estimator. The comparison in favour of the standard normalized estimator is obtained by the mean squared error. We conclude by providing, for the first time, the general asymptotic normalities through some regularity assumptions for both (un)normalized associated-kernel density estimators. The Gumbel, Weibull, gamma, lognormal, and other associated kernels are required for illustrating theoretically and numerically some of our results with an application to original data of automobile claim amounts from Covéa Affinity.
Origine : Fichiers produits par l'(les) auteur(s)