Linear Models for Functional Responses

Abstract

In this second chapter on the functional linear model, the dependent or response variable is functional. We first consider a situation in which all of the independent variables are scalar and in particular look at two functional analyses of variance.

When one or more of the independent variables is also function, we have two possible classes of linear models. The simpler case is called concurrent, where the value of the response variable y(t) is predicted solely by the values of one or more functional covariates at the same time t. The more general case where functional variables contribute to the prediction for all possible time values s is briefly reviewed.