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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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    Cited by:

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    2. 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.
    3. 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.
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    6. 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.
    7. Krzyśko Mirosław & Smaga Łukasz, 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.
    8. 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).
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    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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