Variable selection for functional linear models with strong heredity constraint

Sanying Feng, Menghan Zhang, Tiejun Tong*

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

3 Citations (Scopus)

Abstract

In this paper, we consider the variable selection problem in functional linear regression with interactions. Our goal is to identify relevant main effects and corresponding interactions associated with the response variable. Heredity is a natural assumption in many statistical models involving two-way or higher-order interactions. Inspired by this, we propose an adaptive group Lasso method for the multiple functional linear model that adaptively selects important single functional predictors and pairwise interactions while obeying the strong heredity constraint. The proposed method is based on the functional principal components analysis with two adaptive group penalties, one for main effects and one for interaction effects. With appropriate selection of the tuning parameters, the rates of convergence of the proposed estimators and the consistency of the variable selection procedure are established. Simulation studies demonstrate the performance of the proposed procedure and a real example is analyzed to illustrate its practical usage.
Original languageEnglish
Pages (from-to)321-339
Number of pages19
JournalAnnals of the Institute of Statistical Mathematics
Volume74
Issue number2
Early online date28 Apr 2021
DOIs
Publication statusPublished - Apr 2022

Scopus Subject Areas

  • Statistics and Probability

User-Defined Keywords

  • Functional linear model
  • Heredity structure
  • Interaction effect
  • Main effect
  • Multiple functional predictors
  • Variable selection

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