Functional data analysis tools, such as function-on-function regression models, have received considerable attention in various scientific fields because of their observed high-dimensional and complex data structures. Several statistical procedures, including least squares, maximum likelihood, and maximum penalized likelihood, have been proposed to estimate such function-on-function regression models. However, these estimation techniques produce unstable estimates in the case of degenerate functional data or are computationally intensive. To overcome these issues, we proposed a partial least squares approach to estimate the model parameters in the function-on-function regression model. In the proposed method, the B-spline basis functions are utilized to convert discretely observed data into their functional forms. Generalized cross-validation is used to control the degrees of roughness. The finite-sample performance of the proposed method was evaluated using several Monte-Carlo simulations and an empirical data analysis. The results reveal that the proposed method competes favorably with existing estimation techniques and some other available function-on-function regression models, with significantly shorter computational time.

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关于函数对函数回归：偏最小二乘法

功能数据分析工具（如功能对功能回归模型）因其观察到的高维和复杂数据结构而在各个科学领域引起了相当大的关注。已经提出了几种统计程序，包括最小二乘，最大似然和最大惩罚似然，以估计这种功能函数回归模型。但是，在功能数据退化的情况下，这些估计技术会产生不稳定的估计，或者计算量很大。为了克服这些问题，我们提出了一种偏最小二乘方法来估计函数对函数回归模型中的模型参数。在建议的方法中，B-样条基函数用于将离散观察到的数据转换为其功能形式。通用交叉验证用于控制粗糙度。使用几种蒙特卡洛模拟和经验数据分析评估了该方法的有限样本性能。结果表明，所提出的方法与现有的估计技术和其他一些可用的函数对函数回归模型相竞争，计算时间大大缩短。