Wang Zhanfeng, Dong Hao, Ma Ping, Wang Yuedong
International Institute of Finance, The School of Management, University of Science and Technology of China.
Department of Statistics and Applied Probability, University of California, Santa Barbara.
J Comput Graph Stat. 2022;31(3):835-845. doi: 10.1080/10618600.2022.2037434. Epub 2022 Mar 28.
Regression models with a functional response and functional covariate have received significant attention recently. While various nonparametric and semiparametric models have been developed, there is an urgent need for model selection and diagnostic methods. In this article, we develop a unified framework for estimation and model selection in nonparametric function-on-function regression. We propose a general nonparametric functional regression model with the model space constructed through smoothing spline analysis of variance (SS ANOVA). The proposed model reduces to some of the existing models when selected components in the SS ANOVA decomposition are eliminated. We propose new estimation procedures under either or penalty and show that the combination of the SS ANOVA decomposition and penalty provides powerful tools for model selection and diagnostics. We establish consistency and convergence rates for estimates of the regression function and each component in its decomposition under both the and penalties. Simulation studies and real examples show that the proposed methods perform well. Technical details and additional simulation results are available in online supplementary materials.
近期，具有函数响应和函数协变量的回归模型受到了广泛关注。尽管已经开发了各种非参数和半参数模型，但迫切需要模型选择和诊断方法。在本文中，我们为非参数函数对函数回归中的估计和模型选择开发了一个统一框架。我们提出了一个一般的非参数函数回归模型，其模型空间通过平滑样条方差分析（SS ANOVA）构建。当消除SS ANOVA分解中的选定组件时，所提出的模型简化为一些现有模型。我们提出了在(L_1)或(L_2)惩罚下的新估计程序，并表明SS ANOVA分解和(L_1)惩罚的组合为模型选择和诊断提供了强大的工具。我们在(L_1)和(L_2)惩罚下建立了回归函数及其分解中每个组件估计的一致性和收敛速度。模拟研究和实际例子表明所提出的方法表现良好。技术细节和额外的模拟结果可在在线补充材料中获得。
