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Generalized additive models for functional data

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  • Manuel Febrero-Bande
  • Wenceslao González-Manteiga

Abstract

The aim of this paper is to extend the ideas of generalized additive models for multivariate data (with known or unknown link function) to functional data covariates. The proposed algorithm is a modified version of the local scoring and backfitting algorithms that allows for the nonparametric estimation of the link function. This algorithm would be applied to predict a binary response example. Copyright Sociedad de Estadística e Investigación Operativa 2013

Suggested Citation

  • 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.
    • Handle: RePEc:spr:testjl:v:22:y:2013:i:2:p:278-292
    DOI: 10.1007/s11749-012-0308-0
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    References listed on IDEAS

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    1. James, Gareth M. & Silverman, Bernard W., 2005. "Functional Adaptive Model Estimation," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 565-576, June.
    2. Horowitz, Joel L, 2001. "Nonparametric Estimation of a Generalized Additive Model with an Unknown Link Function," Econometrica, Econometric Society, vol. 69(2), pages 499-513, March.
    3. Cardot, Hervé & Sarda, Pacal, 2005. "Estimation in generalized linear models for functional data via penalized likelihood," Journal of Multivariate Analysis, Elsevier, vol. 92(1), pages 24-41, January.
    4. Aneiros-Pérez, Germán & Vieu, Philippe, 2006. "Semi-functional partial linear regression," Statistics & Probability Letters, Elsevier, vol. 76(11), pages 1102-1110, June.
    5. Müller, Hans-Georg & Yao, Fang, 2008. "Functional Additive Models," Journal of the American Statistical Association, American Statistical Association, vol. 103(484), pages 1534-1544.
    6. Ferraty, Frédéric & Vieu, Philippe, 2009. "Additive prediction and boosting for functional data," Computational Statistics & Data Analysis, Elsevier, vol. 53(4), pages 1400-1413, February.
    7. Gareth M. James, 2002. "Generalized linear models with functional predictors," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(3), pages 411-432, August.
    8. Goia, Aldo, 2012. "A functional linear model for time series prediction with exogenous variables," Statistics & Probability Letters, Elsevier, vol. 82(5), pages 1005-1011.
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    Citations

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    Cited by:

    1. Kehui Chen & Xiaoke Zhang & Alexander Petersen & Hans-Georg Müller, 2017. "Quantifying Infinite-Dimensional Data: Functional Data Analysis in Action," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 9(2), pages 582-604, December.
    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. Febrero-Bande, Manuel & González-Manteiga, Wenceslao & Prallon, Brenda & Saporito, Yuri F., 2023. "Functional classification of bitcoin addresses," Computational Statistics & Data Analysis, Elsevier, vol. 181(C).
    4. Sinova, Beatriz & Van Aelst, Stefan, 2015. "On the consistency of a spatial-type interval-valued median for random intervals," Statistics & Probability Letters, Elsevier, vol. 100(C), pages 130-136.
    5. 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.
    6. Chiou, Jeng-Min & Yang, Ya-Fang & Chen, Yu-Ting, 2016. "Multivariate functional linear regression and prediction," Journal of Multivariate Analysis, Elsevier, vol. 146(C), pages 301-312.
    7. Manuel Febrero-Bande, 2016. "Comments on: Probability enhanced effective dimension reduction for classifying sparse functional data," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 25(1), pages 35-40, March.
    8. Merve Yasemin Tekbudak & Marcela Alfaro-Córdoba & Arnab Maity & Ana-Maria Staicu, 2019. "A comparison of testing methods in scalar-on-function regression," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 103(3), pages 411-436, September.
    9. Shang, Han Lin, 2013. "Bayesian bandwidth estimation for a nonparametric functional regression model with unknown error density," Computational Statistics & Data Analysis, Elsevier, vol. 67(C), pages 185-198.
    10. Eva Boj & Adrià Caballé & Pedro Delicado & Anna Esteve & Josep Fortiana, 2016. "Global and local distance-based generalized linear models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 25(1), pages 170-195, March.
    11. Qiu, Zhiping & Chen, Jianwei & Zhang, Jin-Ting, 2021. "Two-sample tests for multivariate functional data with applications," Computational Statistics & Data Analysis, Elsevier, vol. 157(C).
    12. Manuel Febrero-Bande, 2016. "Comments on: Probability enhanced effective dimension reduction for classifying sparse functional data," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 25(1), pages 35-40, March.
    13. Álvarez-Liébana, J. & Bosq, D. & Ruiz-Medina, M.D., 2017. "Asymptotic properties of a component-wise ARH(1) plug-in predictor," Journal of Multivariate Analysis, Elsevier, vol. 155(C), pages 12-34.
    14. Liu, Xi & Divani, Afshin A. & Petersen, Alexander, 2022. "Truncated estimation in functional generalized linear regression models," Computational Statistics & Data Analysis, Elsevier, vol. 169(C).
    15. 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.
    16. J. A. Cuesta-Albertos & M. Febrero-Bande & M. Oviedo de la Fuente, 2017. "The $$\hbox {DD}^G$$ DD G -classifier in the functional setting," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 26(1), pages 119-142, March.
    17. Philip T. Reiss & Jeff Goldsmith & Han Lin Shang & R. Todd Ogden, 2017. "Methods for Scalar-on-Function Regression," International Statistical Review, International Statistical Institute, vol. 85(2), pages 228-249, August.
    18. Manuel Febrero-Bande & Pedro Galeano & Wenceslao González-Manteiga, 2017. "Functional Principal Component Regression and Functional Partial Least-squares Regression: An Overview and a Comparative Study," International Statistical Review, International Statistical Institute, vol. 85(1), pages 61-83, April.

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