We consider the functional non-parametric regression model "Y"&equals; "r"(<b>"χ"</b>)&plus;"&epsiv;", where the response "Y" is univariate, <b>"χ"</b> is a functional covariate (i.e. valued in some infinite-dimensional space), and the error "&epsiv;" satisfies "E"("&epsiv;" | <b>"χ"</b>) &equals; 0. For this model, the pointwise...

type="main" xml:id="sjos12048-abs-0001" <title type="main">ABSTRACT</title> <p>For fixed size sampling designs with high entropy, it is well known that the variance of the Horvitz–Thompson estimator can be approximated by the Hájek formula. The interest of this asymptotic variance approximation is that it only involves...</p>

This work proposes an extension of the functional principal components analysis (FPCA) or Karhunen-Loève expansion, which can take into account non-parametrically the effects of an additional covariate. Such models can also be interpreted as non-parametric mixed effect models for functional...