Autore
Salinelli, Ernesto

Titolo
Additive Functional Regression based on Predictive Directions
Periodico
Università degli Studi del Piemonte Orientale 'A. Avogadro' : Facoltà di Economia - Dipartimento di Scienze Economiche e Metodi Quantitativi "SEMEQ" - Quaderni
Anno: 2010 - Fascicolo: 13 - Pagina iniziale: 1 - Pagina finale: 34

In this paper we introduce a flexible approach to approximate the regression function in the case of a functional predictor and a scalar response. Following the Projection Pursuit Regression principle, we derive an additive decomposition which exploits the most interesting projections of the prediction variable to explain the response. On the one hand this approach allows to avoid the well-known curse of dimesionality problem and on the other hand can be used as an exploratory tool for the analysis of functional dataset. The terms of such decomposition are estimated with a procedure combining a spline approximation and the one-dimensional Nadaraya-Watson approach. The good behaviour of our procedure is illustrated from theoretical and practical points of view. Asymptotic results state that the terms in the additive decomposition can be estimated without suffering from the dimensionality problem, while some applications to real and simulated data show the high predictive performance of our method.



Testo completo: http://semeq.unipmn.it/files/WP201013.pdf

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