IDEAS home Printed from https://ideas.repec.org/a/eee/ecosta/v1y2017icp150-166.html
   My bibliography  Save this article

Multinomial functional regression with wavelets and LASSO penalization

Author

Listed:
  • Mousavi, Seyed Nourollah
  • Sørensen, Helle

Abstract

A classification problem with a functional predictor is studied, and it is suggested to use a multinomial functional regression (MFR) model for the analysis. The discrete wavelet transform and LASSO penalization are combined for estimation, and the fitted model is used for classification of new curves with unknown class membership. The MFR approach is applied to two datasets, one regarding lameness detection for horses and another regarding speech recognition. In the applications, as well as in a simulation study, the performance of the MFR approach is compared to that of other methods for supervised classification of functional data, and MFR performs as well or better than the other methods.

Suggested Citation

  • Mousavi, Seyed Nourollah & Sørensen, Helle, 2017. "Multinomial functional regression with wavelets and LASSO penalization," Econometrics and Statistics, Elsevier, vol. 1(C), pages 150-166.
    • Handle: RePEc:eee:ecosta:v:1:y:2017:i:c:p:150-166
    DOI: 10.1016/j.ecosta.2016.09.005
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S2452306216300211
    Download Restriction: Full text for ScienceDirect subscribers only. Contains open access articles
    File URL: https://libkey.io/10.1016/j.ecosta.2016.09.005?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Crainiceanu, Ciprian M. & Staicu, Ana-Maria & Di, Chong-Zhi, 2009. "Generalized Multilevel Functional Regression," Journal of the American Statistical Association, American Statistical Association, vol. 104(488), pages 1550-1561.
    2. Aurore Delaigle & Peter Hall, 2012. "Achieving near perfect classification for functional data," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 74(2), pages 267-286, 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. Cardot, Hervé & Ferraty, Frédéric & Sarda, Pascal, 1999. "Functional linear model," Statistics & Probability Letters, Elsevier, vol. 45(1), pages 11-22, October.
    5. Simon N. Wood, 2011. "Fast stable restricted maximum likelihood and marginal likelihood estimation of semiparametric generalized linear models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 73(1), pages 3-36, January.
    6. Ferraty, F. & Vieu, P., 2003. "Curves discrimination: a nonparametric functional approach," Computational Statistics & Data Analysis, Elsevier, vol. 44(1-2), pages 161-173, October.
    7. Friedman, Jerome H. & Hastie, Trevor & Tibshirani, Rob, 2010. "Regularization Paths for Generalized Linear Models via Coordinate Descent," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 33(i01).
    8. Luo Xiao & Yingxing Li & David Ruppert, 2013. "Fast bivariate P-splines: the sandwich smoother," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 75(3), pages 577-599, June.
    9. Reiss, Philip T. & Ogden, R. Todd, 2007. "Functional Principal Component Regression and Functional Partial Least Squares," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 984-996, September.
    10. repec:wyi:journl:002174 is not listed on IDEAS
    11. J. Goldsmith & S. Greven & C. Crainiceanu, 2013. "Corrected Confidence Bands for Functional Data Using Principal Components," Biometrics, The International Biometric Society, vol. 69(1), pages 41-51, March.
    12. Lee, Eun Ryung & Park, Byeong U., 2012. "Sparse estimation in functional linear regression," Journal of Multivariate Analysis, Elsevier, vol. 105(1), pages 1-17.
    13. Antonio Cuevas & Manuel Febrero & Ricardo Fraiman, 2007. "Robust estimation and classification for functional data via projection-based depth notions," Computational Statistics, Springer, vol. 22(3), pages 481-496, September.
    14. Cristian Preda & Gilbert Saporta & Caroline Lévéder, 2007. "PLS classification of functional data," Computational Statistics, Springer, vol. 22(2), pages 223-235, July.
    15. Tian, Tian Siva & James, Gareth M., 2013. "Interpretable dimension reduction for classifying functional data," Computational Statistics & Data Analysis, Elsevier, vol. 57(1), pages 282-296.
    16. 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.
    17. Gareth M. James & Trevor J. Hastie, 2001. "Functional linear discriminant analysis for irregularly sampled curves," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(3), pages 533-550.
    18. Helle Sørensen & Anders Tolver & Maj Halling Thomsen & Pia Haubro Andersen, 2012. "Quantification of symmetry for functional data with application to equine lameness classification," Journal of Applied Statistics, Taylor & Francis Journals, vol. 39(2), pages 337-360, May.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Pini, Alessia & Sørensen, Helle & Tolver, Anders & Vantini, Simone, 2023. "Local inference for functional linear mixed models," Computational Statistics & Data Analysis, Elsevier, vol. 181(C).
    2. Qin, Yichen & Wang, Linna & Li, Yang & Li, Rong, 2023. "Visualization and assessment of model selection uncertainty," Computational Statistics & Data Analysis, Elsevier, vol. 178(C).
    3. José R. Berrendero & Beatriz Bueno-Larraz & Antonio Cuevas, 2023. "On functional logistic regression: some conceptual issues," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 32(1), pages 321-349, March.
    4. Craig, Sarah J.C. & Kenney, Ana M. & Lin, Junli & Paul, Ian M. & Birch, Leann L. & Savage, Jennifer S. & Marini, Michele E. & Chiaromonte, Francesca & Reimherr, Matthew L. & Makova, Kateryna D., 2023. "Constructing a polygenic risk score for childhood obesity using functional data analysis," Econometrics and Statistics, Elsevier, vol. 25(C), pages 66-86.
    5. Kokoszka, Piotr & Oja, Hanny & Park, Byeong & Sangalli, Laura, 2017. "Special issue on functional data analysis," Econometrics and Statistics, Elsevier, vol. 1(C), pages 99-100.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Han Shang, 2014. "A survey of functional principal component analysis," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 98(2), pages 121-142, April.
    2. 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.
    3. 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.
    4. Chen, Lu-Hung & Jiang, Ci-Ren, 2018. "Sensible functional linear discriminant analysis," Computational Statistics & Data Analysis, Elsevier, vol. 126(C), pages 39-52.
    5. Tian, Tian Siva & James, Gareth M., 2013. "Interpretable dimension reduction for classifying functional data," Computational Statistics & Data Analysis, Elsevier, vol. 57(1), pages 282-296.
    6. repec:cte:wsrepe:ws131312 is not listed on IDEAS
    7. Karl Mosler & Pavlo Mozharovskyi, 2017. "Fast DD-classification of functional data," Statistical Papers, Springer, vol. 58(4), pages 1055-1089, December.
    8. 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.
    9. Fang Yao & Yichao Wu & Jialin Zou, 2016. "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 1-22, March.
    10. M. Aguilera-Morillo & Ana Aguilera & Manuel Escabias & Mariano Valderrama, 2013. "Penalized spline approaches for functional logit regression," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(2), pages 251-277, June.
    11. Fang Yao & Yichao Wu & Jialin Zou, 2016. "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 1-22, March.
    12. Llop, P. & Forzani, L. & Fraiman, R., 2011. "On local times, density estimation and supervised classification from functional data," Journal of Multivariate Analysis, Elsevier, vol. 102(1), pages 73-86, January.
    13. Ciarleglio, Adam & Todd Ogden, R., 2016. "Wavelet-based scalar-on-function finite mixture regression models," Computational Statistics & Data Analysis, Elsevier, vol. 93(C), pages 86-96.
    14. Jonathan E. Gellar & Elizabeth Colantuoni & Dale M. Needham & Ciprian M. Crainiceanu, 2014. "Variable-Domain Functional Regression for Modeling ICU Data," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(508), pages 1425-1439, December.
    15. Kalogridis, Ioannis, 2024. "Robust and adaptive functional logistic regression," Computational Statistics & Data Analysis, Elsevier, vol. 192(C).
    16. Guochang Wang & Xinyuan Song, 2018. "Functional Sufficient Dimension Reduction for Functional Data Classification," Journal of Classification, Springer;The Classification Society, vol. 35(2), pages 250-272, July.
    17. Hongxiao Zhu & Philip J. Brown & Jeffrey S. Morris, 2012. "Robust Classification of Functional and Quantitative Image Data Using Functional Mixed Models," Biometrics, The International Biometric Society, vol. 68(4), pages 1260-1268, December.
    18. Li, Pai-Ling & Chiou, Jeng-Min & Shyr, Yu, 2017. "Functional data classification using covariate-adjusted subspace projection," Computational Statistics & Data Analysis, Elsevier, vol. 115(C), pages 21-34.
    19. Carlo Sguera & Pedro Galeano & Rosa Lillo, 2014. "Spatial depth-based classification for functional data," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(4), pages 725-750, December.
    20. Weishampel, Anthony & Staicu, Ana-Maria & Rand, William, 2023. "Classification of social media users with generalized functional data analysis," Computational Statistics & Data Analysis, Elsevier, vol. 179(C).
    21. Yu-Ru Su & Chong-Zhi Di & Li Hsu, 2017. "Hypothesis testing in functional linear models," Biometrics, The International Biometric Society, vol. 73(2), pages 551-561, June.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:ecosta:v:1:y:2017:i:c:p:150-166. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/econometrics-and-statistics .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.