10.6084/m9.figshare.1056513
Yihong Zhao
Yihong
Zhao
Huaihou Chen
Huaihou
Chen
R. Todd Ogden
R.
Todd Ogden
Wavelet-Based Weighted LASSO and Screening Approaches in Functional Linear Regression
Taylor & Francis Group
2015
Adaptive LASSO
Functional data analysis
Penalized linear regression
Screening strategies
Wavelet regression
2015-10-08 12:37:18
Dataset
https://tandf.figshare.com/articles/dataset/Wavelet_Based_Weighted_LASSO_and_Screening_Approaches_in_Functional_Linear_Regression/1056513
<p>One useful approach for fitting linear models with scalar outcomes and functional predictors involves transforming the functional data to wavelet domain and converting the data-fitting problem to a variable selection problem. Applying the LASSO procedure in this situation has been shown to be efficient and powerful. In this article, we explore two potential directions for improvements to this method: techniques for prescreening and methods for weighting the LASSO-type penalty. We consider several strategies for each of these directions which have never been investigated, either numerically or theoretically, in a functional linear regression context. We compare the finite-sample performance of the proposed methods through both simulations and real-data applications with both 1D signals and 2D image predictors. We also discuss asymptotic aspects. We show that applying these procedures can lead to improved estimation and prediction as well as better stability. Supplementary materials for this article are available online.</p>