On robust nonparametric regression estimation for a functional regressor

Strong convergence of robust equivariant nonparametric functional regression estimators

“…where w i (x) are defined in (2). Among other results, in Section 4, we obtain uniform strong convergence rates for F (y|X = x) over R × S H with S H ⊂ H a compact set, generalizing the results in Ferraty et al…”

“…However, even if the mean and the median are scale equivariant, this property does not hold for M −location estimators unless a preliminary robust scale estimator is used to scale the residuals. The same holds for the robust nonparametric regression estimators considered in Azzedine et al (2008). To ensure scale equivariance and robustness, a robust scale estimator needs to be used to decide which responses may be considered as atypical, so that their effect can be downweighted.…”

“…On one hand, we generalize the proposal given in the Euclidean case by Boente and Fraiman (1989) to provide robust equivariant estimators for the regression function in the functional case, that is, in the case where the covariates are in an infinite dimensional space. On the other hand, we extend the proposal given in Azzedine et al (2008) to allow for an unknown scale and heteroscedastic models.…”

Asymptotic normality of a robust estimator of the regression function for functional time series data

“…Cardot, Crambes, and Sarda (2004) used this robust approach to consider the linear model of regression quantile with explanatory variable taking values in a Hilbert space. Recently, Azzeddine, Laksaci, and Ould Saïd (2008) obtained a rate for the almost complete convergence of the robust nonparametric regression estimator when the regressors are functional. These results are extended to the dependent case by Attouch, Laksaci, and Ould Saïd (submitted for publication).…”

Nonparametric M-Estimation for Functional Spatial Data

“…He studied the median estimation (without conditioning) of the distribution of a random variable taking its values in a Banach space. Azzedine et al (2008) adapts to the functional data the local M-estimator of Collomb and Härdle (1986). They established the almost complete convergence of the adapted estimate in the i.i.d.…”