Partial functional linear regression based on the Stacking and RKHS
DOI:
https://doi.org/10.54097/pt6gjr59Keywords:
Functional Data Regression, Nonlinear Relationship Fitting, Ensemble Learning, Truncation Number.Abstract
Functional regression models represent a crucial research area within functional data analysis. To enhance the flexibility of the model, this paper proposes a partial functional linear regression model based on ensemble learning and kernel techniques. On one hand, this method effectively models the relationship between non-linear predictor variables and scalar response variables by employing the Reproducing Kernel Hilbert Space. On the other hand, it utilizes Functional Principal Component Analysis to approximate and estimate functional predictor variables, and addresses the selection of truncation numbers through the stacking framework. In the stacking framework, the meta model takes a model-free form, further increasing the flexibility of the model and effectively balancing the variance and bias of the prediction model. The results of simulation experiments and real-world data analysis demonstrate that the proposed method is more competitive compared to traditional benchmark methods.
Downloads
References
[1] Wu, H. (2023). Robust variable selection in partial linear models with functional data and its application (Doctoral dissertation). Chongqing Technology and Business University.
[2] Jin, X. (2021). Several Methods of Functional Data Analysis. Modern Computer, 27(34),77-80.
[3] Liu, Z. (2020). Functional Data Classification Methods and Their Applications (Doctoral dissertation). Hefei University of Technology.
[4] Zhu, J. (2024). Estimation of High-Dimensional Functional Linear Models Based on Dynamic Principal Components (Doctoral dissertation). Zhejiang University of Finance and Economics.
[5] Wang, H., Huang, L., Wang, S. (2016). Generalized linear regression model based on functional data. Journal of Beijing University of Aeronautics and Astronautics, 42(1), 8-12.
[6] Wang, Q. (2020). Research and application of functional principal component analysis and functional linear regression models (Doctoral dissertation). Chongqing Technology and Business University.
[7] Huang, H., Liu, Y., Ma, Y., et al. (2024). Prediction of soluble solid content in mature apples based on visible/near-infrared spectroscopy and functional linear regression models. Spectroscopy and Spectral Analysis, 44(7), 1905-1912.
[8] Zhang, H., Zhu, Y. (2017). Triangular spline estimation for functional linear regression models. Journal of Yunnan University for Nationalities (Natural Science Edition), 26(6), 475-477.
[9] Jin, T. (2023). Change-point study of functional linear regression models based on Group Lasso (Master’s thesis). Zhejiang University of Finance and Economics.
[10] Liu, X., Ma, H. (2023). Change-point testing in functional linear regression models. Applied Probability and Statistics, 39(4), 475-490.
[11] Yu, P., Du, J., Zhang, Z. (2017). Partial functional linear additive quantile regression models. Systems Science and Mathematical Sciences, 37(5), 1335-1350.
[12] Wang, D., et al. (2022). Functional linear regression with mixed predictors. Journal of Machine Learning Research, 23, 1-94.
[13] Yang, W., Qin, L. (2024). Functional partial linear models based on residual function principal components and their applications. Engineering Economics, 34(11), 33-45.
[14] Hu, Y. (2022). Robust estimation of partial functional linear regression models (Master’s thesis). Guizhou University.
[15] Wen, L. (2022). Homogeneity of variance testing in partial functional linear regression models (Master’s thesis). Beijing University of Technology.
[16] Zhu, R., Zou, G., Zhang, X. (2018). Model averaging methods for partial functional linear models. Systems Science and Mathematical Sciences, 38(7), 777-800.
Downloads
Published
Issue
Section
License
Copyright (c) 2025 Highlights in Science, Engineering and Technology
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
How to Cite
