Scalar-on-Function Relative Error Regression for Weak Dependent Case
Analyzing the co-variability between the Hilbert regressor and the scalar output variable is crucial in functional statistics. In this contribution, the kernel smoothing of the Relative Error Regression (RE-regression) is used to resolve this problem. Precisely, we use the relative square error to e...
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MDPI AG
2023-06-01
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| Series: | Axioms |
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| Online Access: | https://www.mdpi.com/2075-1680/12/7/613 |
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| author | Zouaoui Chikr Elmezouar Fatimah Alshahrani Ibrahim M. Almanjahie Zoulikha Kaid Ali Laksaci Mustapha Rachdi |
| author_facet | Zouaoui Chikr Elmezouar Fatimah Alshahrani Ibrahim M. Almanjahie Zoulikha Kaid Ali Laksaci Mustapha Rachdi |
| author_sort | Zouaoui Chikr Elmezouar |
| collection | DOAJ |
| description | Analyzing the co-variability between the Hilbert regressor and the scalar output variable is crucial in functional statistics. In this contribution, the kernel smoothing of the Relative Error Regression (RE-regression) is used to resolve this problem. Precisely, we use the relative square error to establish an estimator of the Hilbertian regression. As asymptotic results, the Hilbertian observations are assumed to be quasi-associated, and we demonstrate the almost complete consistency of the constructed estimator. The feasibility of this Hilbertian model as a predictor in functional time series data is discussed. Moreover, we give some practical ideas for selecting the smoothing parameter based on the bootstrap procedure. Finally, an empirical investigation is performed to examine the behavior of the RE-regression estimation and its superiority in practice. |
| first_indexed | 2024-03-11T01:18:40Z |
| format | Article |
| id | doaj.art-77c1aef31f9142e19e7572c7bd333675 |
| institution | Directory Open Access Journal |
| issn | 2075-1680 |
| language | English |
| last_indexed | 2024-03-11T01:18:40Z |
| publishDate | 2023-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj.art-77c1aef31f9142e19e7572c7bd3336752023-11-18T18:16:59ZengMDPI AGAxioms2075-16802023-06-0112761310.3390/axioms12070613Scalar-on-Function Relative Error Regression for Weak Dependent CaseZouaoui Chikr Elmezouar0Fatimah Alshahrani1Ibrahim M. Almanjahie2Zoulikha Kaid3Ali Laksaci4Mustapha Rachdi5Department of Mathematics, College of Science, King Khalid University, Abha 62223, Saudi ArabiaDepartment of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, Riyadh 11671, Saudi ArabiaDepartment of Mathematics, College of Science, King Khalid University, Abha 62223, Saudi ArabiaDepartment of Mathematics, College of Science, King Khalid University, Abha 62223, Saudi ArabiaDepartment of Mathematics, College of Science, King Khalid University, Abha 62223, Saudi ArabiaLaboratory AGEIS, University of Grenoble Alpes, UFR SHS, BP. 47, Cedex 09, F38040 Grenoble, FranceAnalyzing the co-variability between the Hilbert regressor and the scalar output variable is crucial in functional statistics. In this contribution, the kernel smoothing of the Relative Error Regression (RE-regression) is used to resolve this problem. Precisely, we use the relative square error to establish an estimator of the Hilbertian regression. As asymptotic results, the Hilbertian observations are assumed to be quasi-associated, and we demonstrate the almost complete consistency of the constructed estimator. The feasibility of this Hilbertian model as a predictor in functional time series data is discussed. Moreover, we give some practical ideas for selecting the smoothing parameter based on the bootstrap procedure. Finally, an empirical investigation is performed to examine the behavior of the RE-regression estimation and its superiority in practice.https://www.mdpi.com/2075-1680/12/7/613complete convergence (a.co.)relative error regressionnonparametric predictionkernel methodbandwidth parameterfunctional data |
| spellingShingle | Zouaoui Chikr Elmezouar Fatimah Alshahrani Ibrahim M. Almanjahie Zoulikha Kaid Ali Laksaci Mustapha Rachdi Scalar-on-Function Relative Error Regression for Weak Dependent Case Axioms complete convergence (a.co.) relative error regression nonparametric prediction kernel method bandwidth parameter functional data |
| title | Scalar-on-Function Relative Error Regression for Weak Dependent Case |
| title_full | Scalar-on-Function Relative Error Regression for Weak Dependent Case |
| title_fullStr | Scalar-on-Function Relative Error Regression for Weak Dependent Case |
| title_full_unstemmed | Scalar-on-Function Relative Error Regression for Weak Dependent Case |
| title_short | Scalar-on-Function Relative Error Regression for Weak Dependent Case |
| title_sort | scalar on function relative error regression for weak dependent case |
| topic | complete convergence (a.co.) relative error regression nonparametric prediction kernel method bandwidth parameter functional data |
| url | https://www.mdpi.com/2075-1680/12/7/613 |
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