Electronic Journal of Statistics

Ridge regression for the functional concurrent model

Tito Manrique, Christophe Crambes, and Nadine Hilgert

Full-text: Open access

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.

Article information

Source
Electron. J. Statist., Volume 12, Number 1 (2018), 985-1018.

Dates
Received: May 2017
First available in Project Euclid: 15 March 2018

Permanent link to this document
https://projecteuclid.org/euclid.ejs/1521079461

Digital Object Identifier
doi:10.1214/18-EJS1412

Mathematical Reviews number (MathSciNet)
MR3776278

Zentralblatt MATH identifier
06864483

Subjects
Primary: 62J05: Linear regression 62G05: Estimation 62G20: Asymptotic properties
Secondary: 62J07: Ridge regression; shrinkage estimators

Keywords
Functional linear model functional data ridge regression concurrent model varying coefficient model

Rights
Creative Commons Attribution 4.0 International License.

Citation

Manrique, Tito; Crambes, Christophe; Hilgert, Nadine. Ridge regression for the functional concurrent model. Electron. J. Statist. 12 (2018), no. 1, 985--1018. doi:10.1214/18-EJS1412. https://projecteuclid.org/euclid.ejs/1521079461


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