Classical functional linear regression models the relationship between a scalar response and a functional covariate, where the coefficient function is assumed to be identical for all subjects. In this paper, the classical model is extended to allow heterogeneous coefficient functions across different subgroups of subjects. The greatest challenge is that the subgroup structure is usually unknown to us. To this end, we develop a penalization-based approach which innovatively applies the penalized fusion technique to simultaneously determine the number and structure of subgroups and coefficient functions within each subgroup. An effective computational algorithm is derived. We also establish the oracle properties and estimation consistency. Extensive numerical simulations demonstrate its superiority compared to several competing methods. The analysis of an air quality dataset leads to interesting findings and improved predictions.
翻译:经典功能性线性回归模型是标量反应和函数共变法之间的关系,其中假定系数功能对所有科目都是一样的。本文将古典模型扩展,允许不同学科分组的系数功能各异。最大的挑战是我们通常不知道分组结构。为此,我们开发了一种基于惩罚的基于惩罚的方法,以创新的方式运用受罚的聚合技术,同时确定每个分组的分组和系数功能的数目和结构。我们制定了有效的计算算法。我们还建立了神器特性和估计一致性。广泛的数字模拟表明它优于几种相互竞争的方法。对空气质量数据集的分析导致有趣的发现和改进的预测。