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

• Autorzy: Amina Angelika Bouchentouf , Tayeb Djebbouri , Abbes Rabhi , Khadidja Sabri
• Języki publikacji: EN

Abstrakty

EN

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.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Applicationes Mathematicae
• Rocznik: 2014
• Tom: 41
• Numer: 4
• Strony: 301-322

Daty

wydano

2014

Twórcy

autor

Amina Angelika Bouchentouf

• Department of Mathematics, University of Sidi Bel Abbes, P.O. Box 89, Sidi Bel Abbes 22 000, Algeria

autor

Tayeb Djebbouri

• 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

autor

Abbes Rabhi

• Department of Mathematics, University of Sidi Bel Abbes, P.O. Box 89, Sidi Bel Abbes 22 000, Algeria

autor

Khadidja Sabri

• Departement of Mathematics, University of Es-Senia Oran, P.O. Box 1524 Elm'Naouer, Oran 31000, Algeria

Identyfikatory

DOI

10.4064/am41-4-2