Nonparametric estimation of some characteristics of the conditional distribution in single functional index model

Abderrahim Mahiddine; Amina Angelika Bouchentouf; A. Rabhi

doi:10.26637/mjm204/006

Abstract

The aim of this paper is to establish a nonparametric estimation of some characteristics of the conditional distribution. Kernel type estimators for the conditional cumulative distribution function and the successive derivatives of the conditional density are introduced of a scalar response variable Y given a Hilbertian random variable X when the observations are linked with a single-index structure. We establish the pointwise almost complete convergence and the uniform almost complete convergence (with the rate) of the kernel estimate of this model. Asymptotic properties are stated for each of these estimates, and they are applied to the estimations of the conditional mode and conditional quantiles.

Keywords:

Conditional single-index, Conditional cumulative distribution, Derivatives of conditional density, Nonparametric estimation, Conditional mode, Conditional quantile, Kernel estimator, semi-metric choice

Mathematics Subject Classification:

62G07, 62G5, 62G20

Authors Imprint References Funding Related Articles Downloads

Abderrahim Mahiddine Department of Mathematics, Djillali Liabes University, B.P. 89, Sidi Bel Abbes, Algeria.
Amina Angelika Bouchentouf Department of Mathematics, Djillali Liabes University, B.P. 89, Sidi Bel Abbes, Algeria. https://orcid.org/0000-0001-8972-4221
A. Rabhi Department of Mathematics, Djillali Liabes University, B.P. 89, Sidi Bel Abbes, Algeria.

Pages: 392-410
Date Published: 01-10-2014
Vol. 2 No. 04 (2014): Malaya Journal of Matematik (MJM)

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