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Variable selection for functional linear models with strong heredity constraint

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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.

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Acknowledgements

The authors sincerely thank the Editor, Associate Editor, and two anonymous reviewers for their insightful comments and suggestions. Sanying Feng’s research was supported by the National Statistical Science Research Project of China (No. 2019LY18), the Natural Science Foundation of Henan Province, China (No. 212300410412), the Foundation of Henan Educational Committee, China (No. 21A910004), and the Excellent Youth Foundation of Zhengzhou University, China (No. 32210452). Tiejun Tong’s research was supported by the General Research Fund (No. HKBU12303918), the National Natural Science Foundation of China (No. 1207010822), and the Initiation Grant for Faculty Niche Research Areas (No. RC-IG-FNRA/17-18/13) of Hong Kong Baptist University.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Zhengzhou University, Zhengzhou, 450001, China

    Sanying Feng & Menghan Zhang

  2. Department of Mathematics, Hong Kong Baptist University, Kowloon, Hong Kong

    Tiejun Tong

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  1. Sanying Feng
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  2. Menghan Zhang
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  3. Tiejun Tong
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Correspondence to Tiejun Tong.

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Feng, S., Zhang, M. & Tong, T. Variable selection for functional linear models with strong heredity constraint. Ann Inst Stat Math 74, 321–339 (2022). https://doi.org/10.1007/s10463-021-00798-z

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