Partially Linear Generalized Single Index Models for Functional Data (PLGSIMF)

Mohamed Alahiane, Idir Ouassou, Mustapha Rachdi and Philippe Vieu
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Mohamed Alahiane: Ecole Nationale des Sciences Appliquées, Université Cadi Ayyad, Marrakech 40 001, Morocco
Idir Ouassou: Ecole Nationale des Sciences Appliquées, Université Cadi Ayyad, Marrakech 40 001, Morocco
Mustapha Rachdi: Laboratoiry AGEIS, UFR SHS, Université Grenoble Alpes, BP. 47, CEDEX 09, 38040 Grenoble, France
Philippe Vieu: Institut de Mathématiques de Toulouse, Université Paul Sabatier, CEDEX 9, 31062 Toulouse, France

Stats, 2021, vol. 4, issue 4, 1-21

Abstract: Single-index models are potentially important tools for multivariate non-parametric regression analysis. They generalize linear regression models by replacing the linear combination α 0 ⊤ X with a non-parametric component η 0 α 0 ⊤ X , where η 0 ( · ) is an unknown univariate link function. In this article, we generalize these models to have a functional component, replacing the generalized partially linear single index models η 0 α 0 ⊤ X + β 0 ⊤ Z , where α is a vector in I R d , η 0 ( · ) and β 0 ( · ) are unknown functions that are to be estimated. We propose estimates of the unknown parameter α 0 , the unknown functions β 0 ( · ) and η 0 ( · ) and establish their asymptotic distributions, and furthermore, a simulation study is carried out to evaluate the models and the effectiveness of the proposed estimation methodology.

Keywords: asymptotic normality; functional data analysis (FDA); polynomial splines; quasi-likelihood; semi-parametric regression; single-index model (search for similar items in EconPapers)
JEL-codes: C1 C10 C11 C14 C15 C16 (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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