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Wydawnictwa / Czasopisma IMPAN / Applicationes Mathematicae / Wszystkie zeszyty

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

Tom 41 / 2014

Applicationes Mathematicae 41 (2014), 301-322 MSC: Primary 62G05, 62G20; Secondary 62F12, 62H12. DOI: 10.4064/am41-4-2

Streszczenie

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.

Autorzy

• Amina Angelika BouchentoufDepartment of Mathematics
University of Sidi Bel Abbes
P.O. Box 89
Sidi Bel Abbes 22 000, Algeria
e-mail
• Tayeb DjebbouriDepartment of Mathematics and
Computer Sciences
Faculty of Sciences and Technology
University Moulay Tahar-Saida
P.O. Box 138
En-Nasr Saida 20 000, Algeria
e-mail
• Abbes RabhiDepartment of Mathematics
University of Sidi Bel Abbes
P.O. Box 89
Sidi Bel Abbes 22 000, Algeria
e-mail