Many papers deal with structural testing procedures in multivariate regression. More recently, various estimators have been proposed for regression models involving functional explanatory variables. Thanks to these new estimators, we propose a theoretical framework for structural testing...

Additive principal components(APCs) generalize classicalprincipal component analysisto additive nonlinear transformations.Smallest APCsare additive functions of the vectorX=(X1, ..., Xp) minimizing the variance under orthogonality constraints and are characterized as eigenfunctions of an...

We analyze in a regression setting the link between a scalar response and a functional predictor by means of a Functional Generalized Linear Model. We first give a theoretical framework and then discuss identifiability of the model. The functional coefficient of the model is estimated via...

We consider the problem of estimating the regression function in functional linear regression models by proposing a new type of projection estimators which combine dimension reduction and thresholding. The introduction of a threshold rule allows us to get consistency under broad assumptions as...

This paper introduces a new nonparametric estimator based on penalized regression splines for linear operator equations when the data are noisy. A local roughness penalty that relies on local support properties of B-splines is introduced in order to deal with spatial heterogeneity of the...