Geodesic
Strong uniform consistency rates of some characteristics of the conditional distribution estimator in the functional single-index model
Amina Angelika Bouchentouf 1   ; Tayeb Djebbouri 2   ; Abbes Rabhi 1   ; Khadidja Sabri 3
1 Department of Mathematics University of Sidi Bel Abbes P.O. Box 89 Sidi Bel Abbes 22 000, Algeria
2 Department of Mathematics and Computer Sciences Faculty of Sciences and Technology University Moulay Tahar-Saida P.O. Box 138 En-Nasr Saida 20 000, Algeria
3 Departement of Mathematics University of Es-Senia Oran P.O. Box 1524 Elm'Naouer Oran 31000, Algeria
Applicationes Mathematicae, Tome 41 (2014) no. 4, pp. 301-322 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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

Amina Angelika Bouchentouf  1   ; Tayeb Djebbouri  2   ; Abbes Rabhi  1   ; Khadidja Sabri  3

1 Department of Mathematics University of Sidi Bel Abbes P.O. Box 89 Sidi Bel Abbes 22 000, Algeria
2 Department of Mathematics and Computer Sciences Faculty of Sciences and Technology University Moulay Tahar-Saida P.O. Box 138 En-Nasr Saida 20 000, Algeria
3 Departement of Mathematics University of Es-Senia Oran P.O. Box 1524 Elm'Naouer Oran 31000, Algeria 
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     title = {Strong uniform consistency rates of some characteristics of the conditional distribution estimator in the functional single-index model},
     journal = {Applicationes Mathematicae},
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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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