Anticipated and Adaptive Prediction in Functional Discriminant Analysis

Linear discriminant analysis with binary response is considered whenthe predictor is a functional random variableX={Xt,t∈[0,T]},T∈R. Motivatedby a food industry problem, we develop a methodology to anticipate the predictionby determining the smallestT∗,T∗≤T, such thatX∗={Xt,t∈[0,T∗]}andXgive similar predictions. The adaptive prediction concerns the observation of anew curveωon [0,T∗(ω)] instead of [0,T] and answers to the question ”How longshould we observeω(T∗(ω) =?) for having the same prediction as on [0,T] ?”. Weanswer to this question by defining a conservation measure with respect to the classthe new curve is predicted