Locally Sparse Estimator for Functional Linear Regression Models
提出一种基于fSCAD正则化的局部稀疏估计量，能识别系数函数的零子区域且不压缩非零值，理论一致且计算简单，模拟和实际数据表现优异。
A new locally sparse (i.e., zero on some subregions) estimator for coefficient functions in functional linear regression models is developed based on a novel functional regularization technique called “fSCAD.” The nice shrinkage property of fSCAD allows the proposed estimator to locate null subregions of coefficient functions without over shrinking nonzero values of coefficient functions. Additionally, a roughness penalty is incorporated to control the roughness of the locally sparse estimator. Our method is theoretically sounder and computationally simpler than existing methods. Asymptotic analysis reveals that the proposed estimator is consistent and can identify null subregions with probability tending to one. Extensive simulations confirm the theoretical analysis and show excellent numerical performance of the proposed method. Practical merit of locally sparse modeling is demonstrated by two real applications. Supplemental materials for the article are available online.