Ridge regression for the functional concurrent model

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 co...

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Bibliographic Details
Published inElectronic journal of statistics Vol. 12; no. 1; pp. 985 - 1018
Main Authors Manrique, Tito, Crambes, Christophe, Hilgert, Nadine
Format Journal Article
LanguageEnglish
Published Shaker Heights, OH : Institute of Mathematical Statistics 01.01.2018
Subjects
Mathematics
Statistics
concurrent model
varying coefficient model
and phrases: Functional linear model
ridge regression
functional data
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ISSN1935-7524
1935-7524
DOI10.1214/18-EJS1412

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Summary: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.
ISSN:1935-7524
1935-7524
DOI:10.1214/18-EJS1412