Yan Xingyu, Yu Jiaqian, Ding Weiyong, Wang Hao, Zhao Peng
School of Mathematics and Statistics and RIMS, Jiangsu Provincial Key Laboratory of Educational Big Data Science and Engineering, Jiangsu Normal University, Xuzhou, Jiangsu, People's Republic of China.
School of Mathematics and Statistics, Anhui Normal University, Wuhu, People's Republic of China.
J Appl Stat. 2023 Sep 1;51(10):2025-2038. doi: 10.1080/02664763.2023.2253379. eCollection 2024.
Recently, two-way or longitudinal functional data analysis has attracted much attention in many fields. However, little is known on how to appropriately characterize the association between two-way functional predictor and scalar response. Motivated by a mortality study, in this paper, we propose a novel two-way functional linear model, where the response is a scalar and functional predictor is two-way trajectory. The model is intuitive, interpretable and naturally captures relationship between each way of two-way functional predictor and scalar-type response. Further, we develop a new estimation method to estimate the regression functions in the framework of weak separability. The main technical tools for the construction of the regression functions are product functional principal component analysis and iterative least square procedure. The solid performance of our method is demonstrated in extensive simulation studies. We also analyze the mortality dataset to illustrate the usefulness of the proposed procedure.
最近，双向或纵向功能数据分析在许多领域引起了广泛关注。然而，对于如何恰当地刻画双向功能预测变量与标量响应之间的关联，人们了解甚少。受一项死亡率研究的启发，在本文中，我们提出了一种新颖的双向功能线性模型，其中响应是一个标量，功能预测变量是双向轨迹。该模型直观、可解释，并且自然地捕捉了双向功能预测变量的每种方式与标量型响应之间的关系。此外，我们开发了一种新的估计方法，用于在弱可分性框架下估计回归函数。构建回归函数的主要技术工具是乘积功能主成分分析和迭代最小二乘法。我们的方法在广泛的模拟研究中展现出了良好的性能。我们还分析了死亡率数据集，以说明所提出方法的实用性。
