融合回归方法用于重复函数型数据
Fusion regression methods with repeated functional data
AI总结：
针对重复函数型数据，提出两种基于融合惩罚的回归方法，利用邻域或分组结构获得简约系数函数，并通过模拟和脑电图数据验证。
摘要：
本文考虑了具有重复函数型数据的线性回归和分类方法。对于样本中的每个统计单元，在由某种邻域结构（如空间、分组等）关联的不同条件下，随时间观测一个实值参数。提出了两种基于融合惩罚的回归方法，以考虑该结构引起的依赖性。这些方法旨在通过确定相近条件是否与共同的回归系数函数相关联，来获得简约的系数回归函数。第一种方法是基于1-最近邻的变量融合方法论对函数型数据的推广。第二种方法依赖于组融合套索惩罚，该惩罚假设条件具有某种分组结构，并允许组内回归系数函数之间具有同质性。文中给出了数值模拟和脑电图数据的应用。
英文摘要：
Linear regression and classification methods with repeated functional data are considered. For each statistical unit in the sample, a real-valued parameter is observed over time under different conditions related by some neighborhood structure (spatial, group, etc.). Two regression methods based on fusion penalties are proposed to consider the dependence induced by this structure. These methods aim to obtain parsimonious coefficient regression functions, by determining if close conditions are associated with common regression coefficient functions. The first method is a generalization to functional data of the variable fusion methodology based on the 1-nearest neighbor. The second one relies on the group fusion lasso penalty which assumes some grouping structure of conditions and allows for homogeneity among the regression coefficient functions within groups. Numerical simulations and an application of electroencephalography data are presented.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
