Functional Linear Models for Scalar Responses

Abstract

This is the first of two chapters on the functional linear model. Here we have a dependent or response variable whose value is to be predicted or approximated on the basis of a set of independent or covariate variables, and at least one of these is functional in nature. The focus here is on linear models, or functional analogues of linear regression analysis. This chapter is confined to considering the prediction of a scalar response on the basis of one or more functional covariates, as well as possible scalar covariates.

Confidence intervals are developed for estimated regression functions in order to permit conclusions about where along the t axis a covariate plays a strong role in predicting a functional responses. The chapter also offers some permutation tests of hypotheses.