Additive Function-on-Function Regression
研究加性函数对函数回归模型，其中响应变量在特定时间点的均值依赖于该时间点和整个协变量轨迹。提出基于样条基和特征基组合的高效估计方法，并构建预测区间，适用于相关误差、稀疏或不规则设计等实际场景。
We study additive function-on-function regression where the mean response at a particular time point depends on the time point itself, as well as the entire covariate trajectory. We develop a computationally efficient estimation methodology based on a novel combination of spline bases with an eigenbasis to represent the trivariate kernel function. We discuss prediction of a new response trajectory, propose an inference procedure that accounts for total variability in the predicted response curves, and construct pointwise prediction intervals. The estimation/inferential procedure accommodates realistic scenarios, such as correlated error structure as well as sparse and/or irregular designs. We investigate our methodology in finite sample size through simulations and two real data applications. Supplementary Material for this article is available online.