Author(s)

JiaYi Wang^1*, Yuan Chen¹, YanRan Liu¹, HaoDi Lv²

Affiliation(s)

¹School of Economics and Management, Lanzhou University of Technology, Lanzhou 730050, Gansu, China.

²School of Foreign Languages, Lanzhou University of Technology, Lanzhou 730050, Gansu, China.

Corresponding Author

JiaYi Wang

ABSTRACT

This study proposes a Partial Nonlinear Functional Regression Model (PNFLR) specifically designed to handle complex datasets where the Continuous Scalar Response Variable depends on a mixture of Vector-valued Covariates and Functional Covariates. The structural heterogeneity of these predictors is addressed by assuming a hybrid relationship: the vector components follow a standard Linear Association, whereas the functional inputs exhibit a complex Nonlinear Association with the response. To rigorously model this non-linearity within a Reproducing Kernel Hilbert Space (RKHS), the methodology departs from traditional single-kernel methods often characterized by rigid selection bias. Instead, the framework implements Model Averaging through an Ensemble Learning paradigm to facilitate the Adaptive Selection of kernel functions, thereby enhancing model flexibility. To ensure numerical stability and effective Regularization, a Truncated Approximation strategy is utilized. This process involves projecting the high-dimensional functional data onto a finite subspace via Functional Principal Component Basis Expansion, effectively mitigating overfitting risks while retaining essential structural information. By integrating kernel theory with ensemble mechanics, the PNFLR framework bridges the gap between theoretical function estimation and practical predictive modeling. Empirical evaluations on the Tecator dataset confirm that the architecture articulated herein yields superior Generalization Performance and lower error variance compared to conventional benchmark models across various prediction tasks, demonstrating robustness in real-world analytical scenarios.

KEYWORDS

Functional Data Analysis (FDA); Functional regression; Reproducing kernel; Ensemble learning

CITE THIS PAPER

JiaYi Wang, Yuan Chen, YanRan Liu, HaoDi Lv. Partial nonlinear functional regression model: an approach via reproducing kernel and ensemble learning. World Journal of Information Technology. 2026, 4(1): 19-24. DOI: https://doi.org/10.61784/wjit3078.

REFERENCES

[1] Luo Youxi, Deng Nan, Hu Chaozhu, et al. Research and application of functional cumulative logistic regression model. Journal of Central China Normal University (Natural Sciences), 2023, 57(2): 185-194.

[2] Liu Xinyang, Li Xiuying, Geng Fazhan. A nonparametric regression method for functional data based on kernel function. Journal of Changshu Institute of Technology, 2025, 39(2): 103-106.

[3] Yang Jintao, Ling Nengxiang. Estimation of functional nonparametric quantile regression model with randomly censored response variables. Journal of Hefei University of Technology (Natural Science), 2023, 46(5): 709-712.

[4] Tomohisa O, Yukitoshi F, Takuya N. Consistent estimation of strain-rate fields from GNSS velocity data using basis function expansion with ABIC. Earth, Planets and Space, 2021, 73(1).

[5] Li Songxuan, Mao Kejing, Xiao Weiwei. Regression models and applications for partially functional data. Advances in Applied Mathematics, 2023, 12(6): 2758-2764.

[6] Wen Liyu. Homogeneity test of variance for partially functional linear regression model. Beijing: Beijing University of Technology, 2022.

[7] Ling N, Aneiros G, Vieu P. kNN estimation in functional partial linear modeling. Statistical Papers, 2022, 61, 423-444.

[8] Huang Jiewu, Wang Linjie, Chen Xingyue, et al. Research on estimation of partial functional linear models with measurement errors. Journal of Tonghua Normal University, 2025, 46(6): 26-32.

[9] Zhu Rong, Zou Guohua, Zhang Xinyu. Model averaging method for partial functional linear models. Journal of Systems Science and Mathematical Sciences, 2018, 38(7): 24.

[10] Liu Yanxia, Wang Zhihao, Tian Maozai. Composite quantile regression estimation of varying coefficient partially functional linear models. Journal of Mathematical Statistics and Management, 2025(2): 1-13.