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Lasso variable selection in functional regression

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  • Romo Urroz, Juan
  • Lillo Rodríguez, Rosa Elvira
  • Mingotti, Nicola

Abstract

Functional Regression has been an active subject of research in the last two decades but still lacks a secure variable selection methodology. Lasso is a well known effective technique for parameters shrinkage and variable selection in regression problems. In this work we generalize the Lasso technique to select variables in the functional regression framework and show it performs well. In particular, we focus on the case of functional regression with scalar regressors and functional response. Reduce the associated functional optimization problem to a convex optimization on scalars. Find its solutions and stress their interpretability. We apply the technique to simulated data sets as well as to a new real data set: car velocity functions in low speed car accidents, a frequent cause of whiplash injuries. By “Functional Lasso” we discover which car characteristics influence more car speed and which can be considered not relevant

Suggested Citation

  • Romo Urroz, Juan & Lillo Rodríguez, Rosa Elvira & Mingotti, Nicola, 2013. "Lasso variable selection in functional regression," DES - Working Papers. Statistics and Econometrics. WS ws131413, Universidad Carlos III de Madrid. Departamento de Estadística.
  • Handle: RePEc:cte:wsrepe:ws131413
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    File URL: https://e-archivo.uc3m.es/bitstream/handle/10016/16959/ws131413.pdf?sequence=1
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    References listed on IDEAS

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    1. 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. Crawford, F. & Watling, D.P. & Connors, R.D., 2017. "A statistical method for estimating predictable differences between daily traffic flow profiles," Transportation Research Part B: Methodological, Elsevier, vol. 95(C), pages 196-213.
    2. Matsui, Hidetoshi, 2014. "Variable and boundary selection for functional data via multiclass logistic regression modeling," Computational Statistics & Data Analysis, Elsevier, vol. 78(C), pages 176-185.
    3. 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.

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    Keywords

    Computer algebra;

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