Anticipated and adaptive prediction in functional discriminant analysis

Abstract

Linear discriminant analysis with binary response is considered when the predictor is a functional random variable X = {Xt, t ∈ [0, T]}, T ∈ R. Motivated by a food industry problem, we develop a methodology to anticipate the prediction by determining the smallest T*, T* ≤ T, such that X* = {Xt, t ∈ [0, T*]} and X give similar predictions. The adaptive prediction concerns the observation of a new curve ω on [0, T*( ω)] instead of [0, T] and answers to the question "How long should we observe ω (T*( ω) =?) 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. © Springer-Verlag Berlin Heidelberg 2010.