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

Abderrahim Mahiddinea,*, Amina Angelika Bouchentoufb, and Abbes Rabhic

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

Authors :

Abderrahim Mahiddine^a,*, Amina Angelika Bouchentouf^b, and Abbes Rabhi^c

Author Address :

^a,b,cMathematics Laboratory, Djillali Liabes University, P.O.BOX. 89, Sidi Bel Abbes, Algeria.

*Corresponding author.

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 cumultative distribution, Derivatives of conditional density, Nonparametric estimation, Conditional mode, Conditional quantile, Ke

DOI :

Article Info :

Received : March 08, 2014; Accepted : May 21, 2014.