Consistency of recursive nonparametric Kernel estimates for independent functional data

Volume 46 / 2019

Amina Angelika Bouchentouf, Abbes Rabhi, Aboubacar Traore Applicationes Mathematicae 46 (2019), 53-83 MSC: 62G05, 62G99, 62M10. DOI: 10.4064/am2371-9-2018 Published online: 22 March 2019

Abstract

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.

Authors

  • Amina Angelika BouchentoufLaboratory of Mathematics
    University Djillali Liabes of Sidi Bel Abbes
    Sidi Bel Abbes, Algeria
    e-mail
  • Abbes RabhiLaboratory of Mathematics
    University Djillali Liabes of Sidi Bel Abbes
    Sidi Bel Abbes, Algeria
    e-mail
  • Aboubacar TraoreFaculty of Sciences and
    Techniques of Bamako
    Bamako, Mali
    e-mail

Search for IMPAN publications

Query phrase too short. Type at least 4 characters.

Rewrite code from the image

Reload image

Reload image