Consistency of recursive nonparametric Kernel estimates for independent functional data

Amina Angelika Bouchentouf¹ ; Abbes Rabhi¹ ; Aboubacar Traore²

¹ Laboratory of Mathematics University Djillali Liabes of Sidi Bel Abbes Sidi Bel Abbes, Algeria
² Faculty of Sciences and Techniques of Bamako Bamako, Mali

Applicationes Mathematicae, Tome 46 (2019) no. 1, pp. 53-83.

Résumé

We propose a new nonparametric estimator of the conditional hazard function. To this end we define nonparametric estimators of the conditional cumulative distribution and the density functions of a scalar response variable $Y$ given a functional random variable $X.$ The conditional cumulative distribution, density and hazard functions for independent functional data are estimated nonparametrically. Our estimates are based on a recursive approach. We establish under appropriate conditions the almost sure and the quadratic average convergence rates of the resulting hazard rate estimator. Furthermore, a simulation study and an application to a real dataset illustrate our methodology.

Détail

DOI : 10.4064/am2371-9-2018

Keywords: propose nonparametric estimator conditional hazard function end define nonparametric estimators conditional cumulative distribution density functions scalar response variable given functional random variable nbsp conditional cumulative distribution density hazard functions independent functional estimated nonparametrically estimates based recursive approach establish under appropriate conditions almost sure quadratic average convergence rates resulting hazard rate estimator furthermore simulation study application real dataset illustrate methodology