Anticipated and Adaptive Prediction in Functional Discriminant Analysis

Cristian Preda (), Gilbert Saporta () and Mohamed Hadj Mbarek ()
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Cristian Preda: Ecole Polytehnique Universitaire de Lille& Laboratoire Painlevé, UMR 8524 Université des Sciences et Technologies de Lille
Gilbert Saporta: Chaire de statistique appliquée & CEDRIC, CNAM
Mohamed Hadj Mbarek: Institut Supérieur de Gestion de Sousse

A chapter in Proceedings of COMPSTAT'2010, 2010, pp 189-198 from Springer

Abstract: Abstract Linear discriminant analysis with binary response is considered when the predictor is a functional random variable $$X=\{X_{t},t\in [0,T]\}$$ , $$T \in\mathbb{R}$$ . Motivated by a food industry problem, we develop a methodology to anticipate the prediction by determining the smallest $$T^{*}$$ , $$T^{*} \leq T$$ , such that $$X^{*} = \{X_{t}, t\in [0,T^{*}]\}$$ and X give similar predictions. The adaptive prediction concerns the observation of a new curve ω on $$[0, T^{*}(\omega)]$$ instead of [0, T] and answers to the question “How long should we observe ω ( $$T^{*}(\omega)=?$$ ) for having the same prediction as on [0,T] ?”. We answer to this question by defining a conservation measure with respect to the class the new curve is predicted.

Keywords: functional data; discriminant analysis; classification; adaptive prediction (search for similar items in EconPapers)
Date: 2010
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-7908-2604-3_17

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DOI: 10.1007/978-3-7908-2604-3_17

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