Strong uniform consistency rates of some characteristics of the conditional distribution estimator in the functional single-index model

Amina Angelika Bouchentouf, et al. "Strong uniform consistency rates of some characteristics of the conditional distribution estimator in the functional single-index model." Applicationes Mathematicae 41.4 (2014): 301-322. <http://eudml.org/doc/279906>.

@article{AminaAngelikaBouchentouf2014,
abstract = {The aim of this paper is to establish a nonparametric estimate of some characteristics of the conditional distribution. Kernel type estimators for the conditional cumulative distribution function and for the successive derivatives of the conditional density of a scalar response variable Y given a Hilbertian random variable X are introduced when the observations are linked with a single-index structure. We establish the pointwise almost complete convergence and the uniform almost complete convergence (with rate) of the kernel estimator of this model. Asymptotic properties are stated for each of these estimators, and they are applied to the estimation of the conditional mode and conditional quantiles.},
author = {Amina Angelika Bouchentouf, Tayeb Djebbouri, Abbes Rabhi, Khadidja Sabri},
journal = {Applicationes Mathematicae},
keywords = {conditional density estimation; functional Hilbert space; semiparametric estimation; semimetric choice; single-index model; uniform almost complete convergence},
language = {eng},
number = {4},
pages = {301-322},
title = {Strong uniform consistency rates of some characteristics of the conditional distribution estimator in the functional single-index model},
url = {http://eudml.org/doc/279906},
volume = {41},
year = {2014},
}

TY - JOUR
AU - Amina Angelika Bouchentouf
AU - Tayeb Djebbouri
AU - Abbes Rabhi
AU - Khadidja Sabri
TI - Strong uniform consistency rates of some characteristics of the conditional distribution estimator in the functional single-index model
JO - Applicationes Mathematicae
PY - 2014
VL - 41
IS - 4
SP - 301
EP - 322
AB - The aim of this paper is to establish a nonparametric estimate of some characteristics of the conditional distribution. Kernel type estimators for the conditional cumulative distribution function and for the successive derivatives of the conditional density of a scalar response variable Y given a Hilbertian random variable X are introduced when the observations are linked with a single-index structure. We establish the pointwise almost complete convergence and the uniform almost complete convergence (with rate) of the kernel estimator of this model. Asymptotic properties are stated for each of these estimators, and they are applied to the estimation of the conditional mode and conditional quantiles.
LA - eng
KW - conditional density estimation; functional Hilbert space; semiparametric estimation; semimetric choice; single-index model; uniform almost complete convergence
UR - http://eudml.org/doc/279906
ER -