Linear Regression Models for Functional Data

Abstract

This paper addresses a specific case of regression analysis: the predictor is a random curve and the response is a scalar. We consider three models: the functional linear model, the functional generalized linear model and functional linear regression on quantiles. Spline functions are used to build estimators which minimize a penalized criterion. The method is illustrated by means of real data examples. Then, we give asymptotics results for these estimators.