Linear prediction in functional data analysis

In this paper we introduce a new perspective of linear prediction in the functional data context that predicts a scalar response by observing a functional predictor. This perspective broadens the scope of functional linear prediction currently in the literature, which is exclusively focused on the functional linear regression model. It also provides a natural link to the classical linear prediction theory. Based on this formulation, we derive the convergence rate of the optimal mean squared predictor. (C) 2012 Elsevier B.V. All rights reserved.