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We develop new estimation results for the functional relationship between a regressor and a response which are functions indexed by time or by spatial locations. The regressor is assumed to belong ...

This article deals with the equivariant non parametric robust regression estimation for stationary ergodic processes valued in F×R, where F is a semi-metric space. We consider a new robust regressi...

L1-norm approach is used to construct the local linear estimator of the spatial regression quantile for functional regressors. Under mixing spatial condition, we establish the almost complete conve...

Under a nonparametric robust regression model, we consider the problem of estimating the score function ψ x for a fixed x in a functional space and with unknown scale parameter. The principal aim of this work is to establish the asymptotic normality of this estimator for a stationary ergodic process without any use of traditional mixing conditions.

We consider a new estimator of the quantile function of a scalar response variable given a functional random variable. This new estimator is based on the $$L_1$$ approach. Under standard assumptions, we prove the almost-complete consistency as well as the asymptotic normality of this estimator. This new approach is also illustrated through some simulated data and its superiority, compared to the classical method, has been proved for practical purposes.

A nonparametric local linear estimator of the conditional quantiles of a scalar response variable Y given a random variable X taking values in a semi-metric space. We establish the almost complete consistency and the asymptotic normality of this estimate. We prove that the asymptotic proprieties of this estimate are closely related to some topological characteristics of the data. Finally, a Monte Carlo study is carried out to evaluate the performance of this estimate.

Let (Zi=(Xi,Yi),i∈ZN) be a F×R-valued measurable strictly stationary spatial process, where F is a semi-metric space. We study a kernel estimator of the conditional mode of the univariate response variable Yi given the functional variable Xi. The main aim of this paper is to prove the almost complete convergence (with rate) of this estimate

Resume Dans cette Note, nous etudions la liaison entre une variable aleatoire reelle Y et une variable fonctionnelle X via lʼestimation de quantiles conditionnels. Plus precisement, nous considerons un champ aleatoire ( Z i = ( X i , Y i ) i ∈ N N , N ⩾ 1 ) de meme loi que ( X , Y ) et nous etablissons la convergence en moyenne dʼordre p dʼun estimateur a noyau du quantile conditionnel de Y i sachant X i .