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Variable selection for functional regression models via the L1 regularization

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  • Matsui, Hidetoshi
  • Konishi, Sadanori

Abstract

In regression analysis, L1 regularizations such as the lasso or the SCAD provide sparse solutions, which leads to variable selection. We consider the variable selection problem where variables are given as functional forms, using L1 regularization. In order to select functional variables each of which is controlled by multiple parameters, we treat parameters as grouped parameters and then apply the group SCAD. A crucial issue in the regularization method is the choice of regularization parameters. We derive a model selection criterion for evaluating the model estimated by the regularization method via the group SCAD penalty. Results of simulation and real data analysis show the effectiveness of the proposed modeling strategy.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:csdana:v:55:y:2011:i:12:p:3304-3310
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    References listed on IDEAS

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    2. Gregorutti, Baptiste & Michel, Bertrand & Saint-Pierre, Philippe, 2015. "Grouped variable importance with random forests and application to multiple functional data analysis," Computational Statistics & Data Analysis, Elsevier, vol. 90(C), pages 15-35.
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    6. Mingotti, Nicola & Lillo Rodríguez, Rosa Elvira & Romo, Juan, 2013. "Lasso variable selection in functional regression," DES - Working Papers. Statistics and Econometrics. WS ws131413, Universidad Carlos III de Madrid. Departamento de Estadística.
    7. 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.
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    11. Fan, Zhaohu & Reimherr, Matthew, 2017. "High-dimensional adaptive function-on-scalar regression," Econometrics and Statistics, Elsevier, vol. 1(C), pages 167-183.
    12. Mirshani, Ardalan & Reimherr, Matthew, 2021. "Adaptive function-on-scalar regression with a smoothing elastic net," Journal of Multivariate Analysis, Elsevier, vol. 185(C).
    13. 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.
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