Strong uniform consistency rates of some characteristics of the conditional distribution estimator in the functional single-index model
Applicationes Mathematicae, Tome 41 (2014) no. 4, pp. 301-322
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
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.
DOI :
10.4064/am41-4-2
Keywords:
paper establish nonparametric estimate characteristics conditional distribution kernel type estimators conditional cumulative distribution function successive derivatives conditional density scalar response variable given hilbertian random variable introduced observations linked single index structure establish pointwise almost complete convergence uniform almost complete convergence rate kernel estimator model asymptotic properties stated each these estimators applied estimation conditional mode conditional quantiles
Affiliations des auteurs :
Amina Angelika Bouchentouf 1 ; Tayeb Djebbouri 2 ; Abbes Rabhi 1 ; Khadidja Sabri 3
@article{10_4064_am41_4_2, author = {Amina Angelika Bouchentouf and Tayeb Djebbouri and Abbes Rabhi and Khadidja Sabri}, title = {Strong uniform consistency rates of some characteristics of the conditional distribution estimator in the functional single-index model}, journal = {Applicationes Mathematicae}, pages = {301--322}, publisher = {mathdoc}, volume = {41}, number = {4}, year = {2014}, doi = {10.4064/am41-4-2}, zbl = {1308.62058}, language = {en}, url = {http://geodesic.mathdoc.fr/articles/10.4064/am41-4-2/} }
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 SP - 301 EP - 322 VL - 41 IS - 4 PB - mathdoc UR - http://geodesic.mathdoc.fr/articles/10.4064/am41-4-2/ DO - 10.4064/am41-4-2 LA - en ID - 10_4064_am41_4_2 ER -
%0 Journal Article %A Amina Angelika Bouchentouf %A Tayeb Djebbouri %A Abbes Rabhi %A Khadidja Sabri %T Strong uniform consistency rates of some characteristics of the conditional distribution estimator in the functional single-index model %J Applicationes Mathematicae %D 2014 %P 301-322 %V 41 %N 4 %I mathdoc %U http://geodesic.mathdoc.fr/articles/10.4064/am41-4-2/ %R 10.4064/am41-4-2 %G en %F 10_4064_am41_4_2
Amina Angelika Bouchentouf; Tayeb Djebbouri; Abbes Rabhi; Khadidja Sabri. Strong uniform consistency rates of some characteristics of the conditional distribution estimator in the functional single-index model. Applicationes Mathematicae, Tome 41 (2014) no. 4, pp. 301-322. doi: 10.4064/am41-4-2
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