Functional linear models

Abstract

In this chapter we review some important ideas related to the functional linear model. Like its multivariate counterpart, this model has been developed in various directions, and has been found to be extremely useful in a broad range of applications. The relevant research is very rich and multifaceted, and we do not aim at a full review of the very extensive literature on this subject. Our objective in this chapter is to explain briefly the general ideas and point to some recent advances. Some additional references are given in Section 8.7. Our choice of topics is partially motivated by the the methodology presented in Chapters 9, 11 and 10. Practically all inferential tool for the functional linear model have been developed under the assumption that the regressor/response pairs, (X _i , Y _i ), are independent. They must therefore be applied with care to functional data obtained over time or space.