论文标题
关于功能线性模型的一般定义
On a general definition of the functional linear model
论文作者
论文摘要
提出了具有功能（随机）解释变量$ x = x（t），t $中的线性模型的一般公式，并提出了标量响应y。它包括基于空间$ l^2 [0,1] $的内部产品的标准功能线性模型，作为一种特殊情况。它还包括所有假定y的模型（最多可添加噪声）是边缘变量x（t_j）的有限或可数集合的线性组合，$ t_j \ in t $或有限的x线性组合x的线性组合。x的线性预测可以用rkhs space cencor covar censifience（coval）covar conscience coval censifience covar centiquar censifcience。证明了一些一致性结果。给出了一些实验结果，以表明在统一的框架中考虑了基于有限数量的边际$ x（t_j）$的线性模型。
A general formulation of the linear model with functional (random) explanatory variable $X = X(t), t \in T$ , and scalar response Y is proposed. It includes the standard functional linear model, based on the inner product in the space $L^2[0,1]$, as a particular case. It also includes all models in which Y is assumed to be (up to an additive noise) a linear combination of a finite or countable collections of marginal variables X(t_j), with $t_j\in T$ or a linear combination of a finite number of linear projections of X. This general formulation can be interpreted in terms of the RKHS space generated by the covariance function of the process X(t). Some consistency results are proved. A few experimental results are given in order to show the practical interest of considering, in a unified framework, linear models based on a finite number of marginals $X(t_j)$ of the process $X(t)$.
