变系数部分函数型线性模型的稳健估计

With the rapid development of observation technologies in the information era, there is a growing demand for analyzing multi-source heterogeneous data in fields such as meteorological monitoring, financial analysis, and biomedical research. Such data often exhibit high-dimensional functional characteristics (e.g., curves or images) with strong correlations, posing challenges to traditional statistical methods: ignoring functional features may lead to the curse of dimensionality and overfitting, while fixed-coefficient linear models fail to capture dynamic relationships among variables. The varying-coefficient partial functional linear model addresses these limitations by extending parameters into functions of spatiotemporal or environmental covariates, providing a feasible framework for integrating heterogeneous data features. However, conventional estimation methods for this model remain sensitive to data perturbations.To overcome these challenges, this paper proposes a robust estimation approach based on modal regression. Specifically, the method extracts core features of functional covariates through functional principal component analysis (FPCA), approximates time-varying coefficients using B-spline basis functions, and mitigates outlier impacts by leveraging the inherent robustness of modal regression. Theoretical analysis establishes the asymptotic convergence properties of the proposed estimators, while numerical experiments under diverse error distributions validate the method\'s effectiveness. Results demonstrate that, compared to traditional least squares estimation, our approach achieves enhanced stability in the presence of data disturbances and superior accuracy in model fitting. This study offers a new analytical perspective for combining functional data analysis with varying-coefficient modeling, providing practical insights for data-driven applications involving noise-contaminated observations.