Locally Sparse Estimator for Functional Linear Regression Models |
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Authors: | Zhenhua Lin Jiguo Cao Liangliang Wang Haonan Wang |
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Institution: | 1. Department of Statistical Sciences, University of Toronto, Toronto, ON, Canada;2. Department of Statistics and Actuarial Science, Simon Fraser University, Burnaby, BC, Canada;3. Department of Statistics, Colorado State University, Fort Collins, Colorado |
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Abstract: | 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. |
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Keywords: | B-spline basis Functional data analysis Null region SCAD Smoothing spline |
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