Ridge regression for the functional concurrent model

Abstract

The aim of this paper is to propose estimators of the unknown functional coefficients in the Functional Concurrent Model (FCM). We extend the Ridge Regression method developed in the classical linear case to the functional data framework. Two distinct penalized estimators are obtained: one with a constant regularization parameter and the other with a functional one. We prove the probability convergence of these estimators with rate. Then we study the practical choice of both regularization parameters. Additionally, we present some simulations that show the accuracy of these estimators despite a very low signal-to-noise ratio.