Anticipated and Adaptive Prediction in Functional Discriminant Analysis

Linear discriminant analysis with binary response is considered when the predictor is a functional random variableX = {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.