A generalized -approach for a kernel estimator of conditional quantile with functional regressors: Consistency and asymptotic normality

Abstract

-Saïd. A generalized -approach for a kernel estimator of conditional quantile with functional regressors: Consistency and asymptotic normality. Statistics and Probability Letters, Elsevier, 2009, 79 (8) This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. A C C E P T E D M A N U S C R I P T ACCEPTED MANUSCRIPTA generalized L Abstract: A kernel estimator of the conditional quantile is defined for a scalar response variable given a covariate taking values in a semi-metric space. The approach generalizes the median's L 1 -norm estimator.The almost complete consistency and asymptotic normality are stated.Keywords Asymptotic distribution · functional data · kernel estimate · robust estimation · small balls probability.

Nonparametric multivariate $L_{1}$-median regression estimation with functional covariates

“…Dabo-Niang and Laksaci (2012) stated the convergence in L p -norm. In the same framework, Laksaci et al (2009) estimated the conditional quantile nonparametrically, by adapting the L 1 -norm method. Recently Quintela-del Río and Vieu (2011) have used the same approach proposed by Ferraty et al (2005) to predict future stratospheric ozone concentrations and to estimate return levels of extreme values of tropospheric ozone.…”

Asymptotic results for an L 1-norm kernel estimator of the conditional quantile for functional dependent data with application to climatology

“…The choice of bandwidth is given by (H6). Finally (H3) allows to get the same convergence rate as in the independent case (see Laksaci et al, 2009).…”

“…From Lemma 3.6 in Laksaci et al (2009) n 2 φ x (h)V ar [Λ 1 (u, x)] → p(1 − p)a 2 (x) a 2 1 (x) = [f x (t p (x))σ(x)] 2 as n → ∞ (6.15) whereas the covariance part can be written (using again the sets defined in (6.5) with an adapted m n )…”

“…In an earlier contribution (see Laksaci et al, 2009) we established the asymptotic normality of the L 1 -norm kernel estimator for the independent case. The present work gives a generalization to the dependent case.…”

Estimation non paramétrique de quantiles conditionnels pour des variables fonctionnelles spatialement dépendantes

“…Citons par exemples Ferraty et al [9,10] pour la convergence presque complète et Ezzahrioui et Ould-Said [7] pour la normalité asymptotique. Nous renvoyons à Laksaci et al [14] pour des résultats analogues à ceux présentés dans [7] et [10] mais pour un estimateur alternatif, basé sur l'approche L 1 .…”