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Consistent variable selection for functional regression models

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  • Collazos, Julian A.A.
  • Dias, Ronaldo
  • Zambom, Adriano Z.

Abstract

The dual problem of testing the predictive significance of a particular covariate, and identification of the set of relevant covariates is common in applied research and methodological investigations. To study this problem in the context of functional linear regression models with predictor variables observed over a grid and a scalar response, we consider basis expansions of the functional covariates and apply the likelihood ratio test. Based on p-values from testing each predictor, we propose a new variable selection method, which is consistent in selecting the relevant predictors from set of available predictors that is allowed to grow with the sample size n. Numerical simulations suggest that the proposed variable selection procedure outperforms existing methods found in the literature. A real dataset from weather stations in Japan is analyzed.

Suggested Citation

  • Collazos, Julian A.A. & Dias, Ronaldo & Zambom, Adriano Z., 2016. "Consistent variable selection for functional regression models," Journal of Multivariate Analysis, Elsevier, vol. 146(C), pages 63-71.
    • Handle: RePEc:eee:jmvana:v:146:y:2016:i:c:p:63-71
    DOI: 10.1016/j.jmva.2015.06.007
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    References listed on IDEAS

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    5. repec:cte:wsrepe:ws131413 is not listed on IDEAS
    6. Matsui, Hidetoshi & Konishi, Sadanori, 2011. "Variable selection for functional regression models via the L1 regularization," Computational Statistics & Data Analysis, Elsevier, vol. 55(12), pages 3304-3310, December.
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    Cited by:

    1. Yu, Dengdeng & Zhang, Li & Mizera, Ivan & Jiang, Bei & Kong, Linglong, 2019. "Sparse wavelet estimation in quantile regression with multiple functional predictors," Computational Statistics & Data Analysis, Elsevier, vol. 136(C), pages 12-29.
    2. Wang, Yun & Wang, Haibo & Srinivasan, Dipti & Hu, Qinghua, 2019. "Robust functional regression for wind speed forecasting based on Sparse Bayesian learning," Renewable Energy, Elsevier, vol. 132(C), pages 43-60.
    3. Shuzhi Zhu & Peixin Zhao, 2019. "Tests for the linear hypothesis in semi-functional partial linear regression models," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 82(2), pages 125-148, March.
    4. Mirosław Krzyśko & Łukasz Smaga, 2017. "An Application Of Functional Multivariate Regression Model To Multiclass Classification," Statistics in Transition New Series, Polish Statistical Association, vol. 18(3), pages 433-442, September.
    5. Łukasz Smaga, 2020. "A note on repeated measures analysis for functional data," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 104(1), pages 117-139, March.
    6. Římalová, Veronika & Fišerová, Eva & Menafoglio, Alessandra & Pini, Alessia, 2022. "Inference for spatial regression models with functional response using a permutational approach," Journal of Multivariate Analysis, Elsevier, vol. 189(C).
    7. Aneiros, Germán & Novo, Silvia & Vieu, Philippe, 2022. "Variable selection in functional regression models: A review," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
    8. Łukasz Smaga & Hidetoshi Matsui, 2018. "A note on variable selection in functional regression via random subspace method," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 27(3), pages 455-477, August.
    9. Krzyśko Mirosław & Smaga Łukasz, 2017. "An Application of Functional Multivariate Regression Model to Multiclass Classification," Statistics in Transition New Series, Statistics Poland, vol. 18(3), pages 433-442, September.
    10. Sanying Feng & Menghan Zhang & Tiejun Tong, 2022. "Variable selection for functional linear models with strong heredity constraint," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 74(2), pages 321-339, April.
    11. Vieu, Philippe, 2018. "On dimension reduction models for functional data," Statistics & Probability Letters, Elsevier, vol. 136(C), pages 134-138.

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