Mohamed ALAHIANE

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• Type de publi. : Article dans une revue
• Date de publi. : 26/08/2024
• Auteurs : Mustapha Mr RachdiMohamed AlahianeIdir OuassouAbdelaziz AlahianeLahoucine Hobbad
• Organismes : Université Grenoble Alpes Ecole Nationale des Sciences Appliquées [Marrakech]
• Publié dans Mathematics le 30/10/2020

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Résumé : 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.

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• Type de publi. : Article dans une revue
• Date de publi. : 30/07/2022
• Auteurs : Mohamed AlahianeIdir Ouassou Idir OuassouMustapha Mr RachdiPhilippe Vieu
• Organismes : Ecole Nationale des Sciences Appliquées [Marrakech] Université Grenoble Alpes Institut de Mathématiques de Toulouse UMR5219
• Publié dans Mathematics le 30/10/2020

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Résumé : We study the non-parametric estimation of partially linear generalized single-index functional models, where the systematic component of the model has a flexible functional semi-parametric form with a general link function. We suggest an efficient and practical approach to estimate (I) the single-index link function, (II) the single-index coefficients as well as (III) the non-parametric functional component of the model. The estimation procedure is developed by applying quasi-likelihood, polynomial splines and kernel smoothings. We then derive the asymptotic properties, with rates, of the estimators of each component of the model. Their asymptotic normality is also established. By making use of the splines approximation and the Fisher scoring algorithm, we show that our approach has numerical advantages in terms of the practical efficiency and the computational stability. A computational study on data is provided to illustrate the good practical behavior of our methodology.

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• Type de publi. : Article dans une revue
• Date de publi. : 27/09/2021
• Auteurs : Mohamed AlahianeIdir Ouassou Idir OuassouMustapha Mr RachdiPhilippe Vieu
• Organismes : Ecole Nationale des Sciences Appliquées [Marrakech] Université Grenoble Alpes Institut de Mathématiques de Toulouse UMR5219
• Publié dans Stats le 28/09/2020

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Résumé : Single-index models are potentially important tools for multivariate non-parametric regression analysis. They generalize linear regression models by replacing the linear combination α0⊤X with a non-parametric component η0α0⊤X, where η0(·) 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 η0α0⊤X+β0⊤Z, where α is a vector in IRd, η0(·) and β0(·) are unknown functions that are to be estimated. We propose estimates of the unknown parameter α0, the unknown functions β0(·) and η0(·) 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.

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