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Variable selection in functional additive regression models

Author

Listed:
  • Manuel Febrero-Bande

    (Universidade de Santiago de Compostela)

  • Wenceslao González-Manteiga

    (Universidade de Santiago de Compostela)

  • Manuel Oviedo de la Fuente

    (Universidade de Santiago de Compostela
    Technological Institute for Industrial Mathematics)

Abstract

This paper considers the problem of variable selection in regression models in the case of functional variables that may be mixed with other type of variables (scalar, multivariate, directional, etc.). Our proposal begins with a simple null model and sequentially selects a new variable to be incorporated into the model based on the use of distance correlation proposed by Székely et al. (Ann Stat 35(6):2769–2794, 2007). For the sake of simplicity, this paper only uses additive models. However, the proposed algorithm may assess the type of contribution (linear, non linear, ...) of each variable. The algorithm has shown quite promising results when applied to simulations and real data sets.

Suggested Citation

  • Manuel Febrero-Bande & Wenceslao González-Manteiga & Manuel Oviedo de la Fuente, 2019. "Variable selection in functional additive regression models," Computational Statistics, Springer, vol. 34(2), pages 469-487, June.
    • Handle: RePEc:spr:compst:v:34:y:2019:i:2:d:10.1007_s00180-018-0844-5
    DOI: 10.1007/s00180-018-0844-5
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    References listed on IDEAS

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    1. Du, Pang & Cheng, Guang & Liang, Hua, 2012. "Semiparametric regression models with additive nonparametric components and high dimensional parametric components," Computational Statistics & Data Analysis, Elsevier, vol. 56(6), pages 2006-2017.
    2. Febrero-Bande, Manuel & de la Fuente, Manuel Oviedo, 2012. "Statistical Computing in Functional Data Analysis: The R Package fda.usc," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 51(i04).
    3. Manuel Febrero-Bande & Wenceslao González-Manteiga, 2013. "Generalized additive models for functional data," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(2), pages 278-292, June.
    4. Fan J. & Li R., 2001. "Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1348-1360, December.
    5. Székely, Gábor J. & Rizzo, Maria L., 2013. "The distance correlation t-test of independence in high dimension," Journal of Multivariate Analysis, Elsevier, vol. 117(C), pages 193-213.
    6. Zou, Hui, 2006. "The Adaptive Lasso and Its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1418-1429, December.
    7. Müller, Hans-Georg & Yao, Fang, 2008. "Functional Additive Models," Journal of the American Statistical Association, American Statistical Association, vol. 103(484), pages 1534-1544.
    8. Ferraty, Frédéric & Vieu, Philippe, 2009. "Additive prediction and boosting for functional data," Computational Statistics & Data Analysis, Elsevier, vol. 53(4), pages 1400-1413, February.
    9. Simon N. Wood, 2004. "Stable and Efficient Multiple Smoothing Parameter Estimation for Generalized Additive Models," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 673-686, January.
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    Citations

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    Cited by:

    1. Laura Freijeiro‐González & Manuel Febrero‐Bande & Wenceslao González‐Manteiga, 2022. "A Critical Review of LASSO and Its Derivatives for Variable Selection Under Dependence Among Covariates," International Statistical Review, International Statistical Institute, vol. 90(1), pages 118-145, April.
    2. Aneiros, Germán & Novo, Silvia & Vieu, Philippe, 2022. "Variable selection in functional regression models: A review," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
    3. Germán Aneiros & Ricardo Cao & Philippe Vieu, 2019. "Editorial on the special issue on Functional Data Analysis and Related Topics," Computational Statistics, Springer, vol. 34(2), pages 447-450, June.
    4. François Freddy Ateba & Manuel Febrero-Bande & Issaka Sagara & Nafomon Sogoba & Mahamoudou Touré & Daouda Sanogo & Ayouba Diarra & Andoh Magdalene Ngitah & Peter J. Winch & Jeffrey G. Shaffer & Donald, 2020. "Predicting Malaria Transmission Dynamics in Dangassa, Mali: A Novel Approach Using Functional Generalized Additive Models," IJERPH, MDPI, vol. 17(17), pages 1-16, August.

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