Functional Time Series Analysis Using Single-Index L1-Modal Regression
Abstract
:1. Introduction
2. Robust Estimator of the Modal-Regression in FSI Structure
3. Main Results
- (AS1)
- . Furthermore, as .
- (AS2)
- The functions is of class and such that the following Lipschitz’s condition is satisfied:
- (AS3)
- The sequence satisfies and
- (AS4)
- is a function with support such that .
- (AS5)
- There exists such that
4. Computational Study
5. Real Data Example
6. Conclusions and Prospects
7. The Mathematical Development
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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The White Noise Distribution | n | p | Outliers Case | ||
---|---|---|---|---|---|
Laplace distribution | 50 | 1 | with outliers | 2.43 | 1.37 |
1 | without outliers | 1.06 | 0.51 | ||
4 | with outliers | 7.92 | 2.29 | ||
4 | without outliers | 1.41 | 0.39 | ||
10 | with outliers | 7.82 | 2.92 | ||
10 | without outliers | 1.95 | 0.52 | ||
100 | 1 | with outliers | 2.36 | 1.29 | |
1 | without outliers | 0.98 | 0.43 | ||
4 | with outliers | 7.61 | 2.17 | ||
4 | without outliers | 1.32 | 0.28 | ||
10 | with outliers | 7.66 | 2.84 | ||
10 | without outliers | 1.89 | 0.39 | ||
250 | 1 | with outliers | 2.17 | 1.07 | |
1 | without outliers | 0.84 | 0.32 | ||
4 | with outliers | 7.43 | 2.06 | ||
4 | without outliers | 1.11 | 0.12 | ||
10 | with outliers | 7.32 | 2.52 | ||
10 | without outliers | 1.72 | 0.25 | ||
Weibull distribution | 50 | 1 | with outliers | 4.54 | 2.95 |
1 | without outliers | 1.81 | 0.77 | ||
4 | with outliers | 4.82 | 3.23 | ||
4 | without outliers | 2.43 | 1.03 | ||
10 | with outliers | 5.91 | 3.48 | ||
10 | without outliers | 2.46 | 1.05 | ||
100 | 1 | with outliers | 4.32 | 2.88 | |
1 | without outliers | 1.63 | 0.69 | ||
4 | with outliers | 4.53 | 3.02 | ||
4 | without outliers | 2.01 | 0.85 | ||
10 | with outliers | 5.78 | 3.34 | ||
10 | without outliers | 2.26 | 0.92 | ||
250 | 1 | with outliers | 4.14 | 2.63 | |
1 | without outliers | 1.32 | 0.43 | ||
4 | with outliers | 4.25 | 2.98 | ||
4 | without outliers | 1.93 | 0.71 | ||
10 | with outliers | 5.49 | 3.11 | ||
10 | without outliers | 2.01 | 0.74 | ||
Log-normal distribution | 50 | 1 | with outliers | 6.53 | 1.32 |
1 | without outliers | 2.50 | 0.79 | ||
4 | with outliers | 5.42 | 2.54 | ||
4 | without outliers | 2.62 | 1.12 | ||
10 | with outliers | 6.61 | 2.66 | ||
10 | without outliers | 3.08 | 1.48 | ||
100 | 1 | with outliers 2 | 6.36 | 1.19 | |
1 | without outliers | 2.04 | 0.67 | ||
4 | with outliers | 5.13 | 2.33 | ||
4 | without outliers | 2.39 | 0.98 | ||
10 | with outliers | 6.44 | 2.59 | ||
10 | without outliers | 2.95 | 1.23 | ||
250 | 1 | with outliers 2 | 6.11 | 1.02 | |
1 | without outliers | 1.82 | 0.51 | ||
4 | with outliers | 5.02 | 2.07 | ||
4 | without outliers | 2.14 | 0.71 | ||
10 | with outliers | 6.36 | 2.28 | ||
10 | without outliers | 2.77 | 1.09 |
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Alamari, M.B.; Almulhim, F.A.; Kaid, Z.; Laksaci, A. Functional Time Series Analysis Using Single-Index L1-Modal Regression. Symmetry 2025, 17, 460. https://doi.org/10.3390/sym17030460
Alamari MB, Almulhim FA, Kaid Z, Laksaci A. Functional Time Series Analysis Using Single-Index L1-Modal Regression. Symmetry. 2025; 17(3):460. https://doi.org/10.3390/sym17030460
Chicago/Turabian StyleAlamari, Mohammed B., Fatimah A. Almulhim, Zoulikha Kaid, and Ali Laksaci. 2025. "Functional Time Series Analysis Using Single-Index L1-Modal Regression" Symmetry 17, no. 3: 460. https://doi.org/10.3390/sym17030460
APA StyleAlamari, M. B., Almulhim, F. A., Kaid, Z., & Laksaci, A. (2025). Functional Time Series Analysis Using Single-Index L1-Modal Regression. Symmetry, 17(3), 460. https://doi.org/10.3390/sym17030460