Abstract
Supporting Institution
This work is partially supported by National Natural Science Foundation of China (12401356), National Statistical Science Research Project of China (2022LY089), the Natural Science Foundation of Shanxi normal University (JYCJ2022004),the 2025 Planning Research Topics of Commerce Statistical Society of China (2025STY119) and Postgraduate Education Innovation Program of Shanxi Province (2025XS110).
Project Number
12401356,2022LY089,JYCJ2022004,2025XS110.
References
- [1] J. O. Ramsay and B. W. Silverman, Applied Functional Fata Analysis: Methods and Case Studies, Springer, New York, 2002.
Abstract
The functional quadratic regression model assumes a polynomial, rather than linear relationship between the scalar response variable and a functional predictor variable. This paper focuses on the statistical inference tailored for the functional quadratic expectile regression model. Functional coefficients are approximated by the functional principal component basis functions, and asymptotic properties of estimators are derived under some mild conditions. Furthermore, to inspect the effect of the functional quadratic term on the response variable, we develop an expectile rank score test and establish its asymptotic property. Simulations are conducted to assess the empirical performance of the proposed estimation methods and test statistic. Results indicate that the proposed estimators are comparable to competing estimation methods and the newly proposed expectile rank score test is effective. Finally, the advantages of our methodologies are illustrated using a real-data example.
Keywords
expectile regression expectile rank score test functional quadratic regression model functional principal component analysis
Ethical Statement
This manuscript is original work not previously published and is not being considered elsewhere.
Supporting Institution
Shanxi Normal University
Project Number
12401356,2022LY089,JYCJ2022004,2025XS110.
Thanks
This work is partially supported by National Natural Science Foundation of China (12401356), National Statistical Science Research Project of China (2022LY089), the Natural Science Foundation of Shanxi normal University (JYCJ2022004) and Postgraduate Education Innovation Program of Shanxi Province (2025XS110).
References
- [1] J. O. Ramsay and B. W. Silverman, Applied Functional Fata Analysis: Methods and Case Studies, Springer, New York, 2002.
Details
| Primary Language | English |
|---|---|
| Subjects | Large and Complex Data Theory, Statistical Theory |
| Journal Section | Research Article |
| Authors | |
| Project Number | 12401356,2022LY089,JYCJ2022004,2025XS110. |
| Submission Date | November 16, 2025 |
| Acceptance Date | January 28, 2026 |
| Early Pub Date | February 12, 2026 |
| Publication Date | February 12, 2026 |
| DOI | https://doi.org/10.15672/hujms.1824224 |
| IZ | https://izlik.org/JA38KT67PL |
| Published in Issue | Year 2026 Issue: Advanced Online Publication |
Cite
Aim & Scope
Aim
Hacettepe Journal of Mathematics and Statistics (Formerly: Hacettepe Bulletin of Natural Sciences and Engineering - Series B) is an international, peer-reviewed, open-access journal that publishes high-quality original research articles and occasional comprehensive surveys in all areas of Mathematics and Statistics. The journal is committed to promoting the advancement of mathematical and statistical sciences by providing a platform for researchers to disseminate their findings to a global audience.
As an open-access journal, Hacettepe Journal of Mathematics and Statistics (HJMS) does not charge any article processing or publishing fees, ensuring that high-quality research remains freely accessible to the scientific community. The journal accepts submissions exclusively in English and upholds a rigorous peer-review process to maintain academic excellence.
The journal is widely recognized in the academic community and is indexed in leading databases such as Web of Science (Science Citation Index Expanded), Scopus, and Zentralblatt MATH. With its long-standing history and commitment to scholarly publishing, Hacettepe Journal of Mathematics and Statistics continues to serve as a valuable resource for researchers, academicians, and practitioners in the fields of Mathematics and Statistics.
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