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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. MSC 2010 subject classifications: Primary 62J05, 62G05, 62G20; secondary 62J07.
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Submitted on : Wednesday, June 20, 2018 - 2:17:14 PM
Last modification on : Friday, July 23, 2021 - 10:28:39 AM
Long-term archiving on: : Tuesday, September 25, 2018 - 12:18:36 AM

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Tito Manrique Chuquillanqui, Christophe Crambes, Nadine Hilgert. Ridge regression for the functional concurrent model. Electronic Journal of Statistics , Shaker Heights, OH : Institute of Mathematical Statistics, 2018, 12 (1), pp.985 - 1018. ⟨10.1214/18-EJS1412⟩. ⟨hal-01819398⟩

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