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Average derivative projection pursuit regression

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In this talk one proposes a general framework for projection Pursuit Regression (PPR) that can deal with an explanatory random function X = {X(t); t ∈ I} and a scalar response Y. In doing so we introduce what we call the average derivative operator of the regression. We show that the unknown directions involved in the functional PPR can be viewed as the eigenfunctions of the average derivative operator. This new characterization of the directional parameters greatly simplifies the estimation problem, offers new interpretation of the directional parameters in PPR and solves identifiability issues inherent in such models.

Motivated by recent works focusing on the nonparametric estimation of the directional derivatives of a regression operator, a nonparametric estimator of the average derivative operator is constructed. Asymptotic properties of the introduced estimators are studied and numerical examples are used to illustrate the method and to assess finite sample performance.

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