Locally Sparse Function-on-Function Regression
提出一种局部稀疏的函数对函数回归模型，通过重叠组Lasso惩罚使回归系数在部分定义域上精确为零，平衡了同步与非同步函数模型，并给出高效算法和理论性质。
In functional data analysis, functional linear regression has attracted significant attention recently. Herein, we consider the case where both the response and covariates are functions. There are two available approaches for addressing such a situation: concurrent and nonconcurrent functional models. In the former, the value of the functional response at a given domain point depends only on the value of the functional regressors evaluated at the same domain point, whereas, in the latter, the functional covariates evaluated at each point of their domain have a non null effect on the response at any point of its domain. To balance these two extremes, we propose a locally sparse functional regression model in which the functional regression coefficient is allowed (but not forced) to be exactly zero for a subset of its domain. This is achieved using a suitable basis representation of the functional regression coefficient and exploiting an overlapping group-Lasso penalty for its estimation. We introduce efficient computational strategies based on majorization-minimization algorithms and discuss appealing theoretical properties regarding the model support and consistency of the proposed estimator. We further illustrate the empirical performance of the method through simulations and two applications related to human mortality and bidding in energy markets. Supplementary materials for this article are available online.