Ridge regression for the functional concurrent model
| Autor: | Christophe Crambes, Nadine Hilgert, Tito Manrique |
|---|---|
| Přispěvatelé: | Mathématiques, Informatique et STatistique pour l'Environnement et l'Agronomie (MISTEA), Institut National de la Recherche Agronomique (INRA)-Institut national d’études supérieures agronomiques de Montpellier (Montpellier SupAgro), Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro), Institut Montpelliérain Alexander Grothendieck (IMAG), Université de Montpellier (UM)-Centre National de la Recherche Scientifique (CNRS), ANR-10-LABX-0020,NUMEV,Digital and Hardware Solutions and Modeling for the Environement and Life Sciences(2010), Institut national d’études supérieures agronomiques de Montpellier (Montpellier SupAgro)-Institut National de la Recherche Agronomique (INRA) |
| Jazyk: | angličtina |
| Rok vydání: | 2018 |
| Předmět: |
Statistics and Probability
01 natural sciences Regularization (mathematics) 010104 statistics & probability 62J07 modèle mathématique 62J05 [MATH.MATH-ST]Mathematics [math]/Statistics [math.ST] 0502 economics and business Convergence (routing) ridge regression Applied mathematics 62G05 and phrases: Functional linear model 0101 mathematics [MATH]Mathematics [math] 62G20 functional data 050205 econometrics Mathematics 05 social sciences Estimator Functional linear model Ridge (differential geometry) Regression concurrent model probabilité varying coefficient model Statistics Probability and Uncertainty Constant (mathematics) |
| Zdroj: | Electronic Journal of Statistics 1 (12), 985-1018. (2018) Electronic Journal of Statistics Electronic Journal of Statistics, Shaker Heights, OH : Institute of Mathematical Statistics, 2018, 12 (1), pp.985-1018. ⟨10.1214/18-EJS1412⟩ Electron. J. Statist. 12, no. 1 (2018), 985-1018 Electronic journal of statistics Electronic journal of statistics, Shaker Heights, OH : Institute of Mathematical Statistics, 2018, 12 (1), pp.985-1018. ⟨10.1214/18-EJS1412⟩ |
| ISSN: | 1935-7524 |
| Popis: | International audience; 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. |
| Databáze: | OpenAIRE |
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