Wavelet-Based Weighted LASSO and Screening Approaches in Functional Linear Regression

Yihong Zhao, Huaihou Chen, R. Todd Ogden

Research output: Contribution to journalArticlepeer-review

22 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)655-675
Number of pages21
JournalJournal of Computational and Graphical Statistics
Issue number3
StatePublished - Jul 3 2015
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty
  • Discrete Mathematics and Combinatorics


  • Adaptive LASSO
  • Functional data analysis
  • Penalized linear regression
  • Screening strategies
  • Wavelet regression


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