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A0182
Title: New foundations for functional local linear regression Authors:  Frederic Ferraty - Mathematics Institute of Toulouse (France) [presenting]
Stanislav Nagy - Charles University (Czech Republic)
Abstract: Local linear regression is one of the most popular nonparametric regression method when the predictor is a finite-dimensional covariate. It is well known that the local linear regression outperforms the usual kernel estimator and the literature dealing with this topic is huge. To our knowledge (and surprisingly) there are only two papers extending the local linear regression to the situation when one considers a functional predictor. Problem: the theoretical developments of one of these works is approximative where in the second one, the authors require strong assumptions with respect to the distribution of the functional predictor. Even if the infinite-dimensional feature of the predictor makes challenging the asymptotics in the functional local linear regression, it is clear that this topic is still underdeveloped. The aim is to bring a relevant response by proposing new theoretical developments. As a by-product, we also provide the asymptotics for the Frechet derivative of the functional linear regression operator.