Cross-Validated Functional Generalized Partially Linear Single-Functional Index Model

Mustapha Rachdi, Mohamed Alahiane (), Idir Ouassou, Abdelaziz Alahiane and Lahoucine Hobbad
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Mustapha Rachdi: Laboratory AGEIS, Grenoble Alps University, UFR SHS, BP. 47, Cedex 09, 38040 Grenoble, France
Mohamed Alahiane: Complex Systems Modeling Laboratory, National School of Applied Sciences, Cadi Ayyad University, Av. Abdelkrim Khattabi, BP. 575, Marrakesh 40000, Morocco
Idir Ouassou: Complex Systems Modeling Laboratory, National School of Applied Sciences, Cadi Ayyad University, Av. Abdelkrim Khattabi, BP. 575, Marrakesh 40000, Morocco
Abdelaziz Alahiane: SmartICT Lab, ENSAO, Mohamed Premier University, Oujda 60000, Morocco
Lahoucine Hobbad: Complex Systems Modeling Laboratory, National School of Applied Sciences, Cadi Ayyad University, Av. Abdelkrim Khattabi, BP. 575, Marrakesh 40000, Morocco

Mathematics, 2024, vol. 12, issue 17, 1-22

Abstract: In this paper, we have introduced a functional approach for approximating nonparametric functions and coefficients in the presence of multivariate and functional predictors. By utilizing the Fisher scoring algorithm and the cross-validation technique, we derived the necessary components that allow us to explain scalar responses, including the functional index, the nonlinear regression operator, the single-index component, and the systematic component. This approach effectively addresses the curse of dimensionality and can be applied to the analysis of multivariate and functional random variables in a separable Hilbert space. We employed an iterative Fisher scoring procedure with normalized B-splines to estimate the parameters, and both the theoretical and practical evaluations demonstrated its favorable performance. The results indicate that the nonparametric functions, the coefficients, and the regression operators can be estimated accurately, and our method exhibits strong predictive capabilities when applied to real or simulated data.

Keywords: single-index coefficient; cross-validation; asymptotic normality; Fisher scoring algorithm; functional data analysis (FDA); functional index; quasi-likelihood (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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