Skip to main content
SpringerLink
Log in

A general sparse modeling approach for regression problems involving functional data

  • Conference paper
  • First Online:
Functional Statistics and Related Fields

Part of the book series: Contributions to Statistics ((CONTRIB.STAT.))

  • 1837 Accesses

Abstract

This presentation aims to introduce an approach for dealing with sparse regression models when functional variables are involved in the statistical sample. The idea is not to restrict to any specific variable selection procedure, but rather to present a two-stage methodology allowing to adapt efficiently any multivariate procedure to the functional framework. These ideas can be applied to any kind of functional regression models, including linear, semi-parametric or non-parametric models.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Aneiros, G., Ferraty, F., Vieu, P.: Variable selection in partial linear regression with functional covariate. Statistics 49, 1322–1347 (2015)

    Google Scholar 

  2. Aneiros, G., Vieu, P.: Variable selection in infinite-dimensional problems. Stat. Probab. Lett. 94, 12–20 (2014)

    Google Scholar 

  3. Aneiros, G., Vieu, P.: Partial linear modelling with multi-functional covariates. Comput. Stat. 30, 647–671 (2015)

    Google Scholar 

  4. Aneiros, G., Vieu, P.: Sparse nonparametric model for regression with functional covariate. J. Nonparametr. Stat. 28, 839–859 (2016)

    Google Scholar 

  5. Aneiros, G., Vieu, P.: Comments on: Probability enhanced effective dimension reduction for classifying sparse functional data. Test 25, 27–32 (2016)

    Google Scholar 

  6. Belloni, A., Chernozhukov, V., Wang, L.: Pivotal estimation via square-root Lasso in nonparametric regression. Ann. Stat. 42, 757–788 (2014)

    Google Scholar 

  7. Bongiorno, E., Goia, A., Salinelli, E., Vieu, P.: An overview of IWFOS’2014. In: Contributions in Infinite-Dimensional Statistics and Related Topics, 1–6. Esculapio, Bologna (2014)

    Google Scholar 

  8. Bühlmann, P., van de Geer, S.: Statistics for High-Dimensional Data. Methods, Theory and Applications. Springer, Heidelberg (2011)

    Google Scholar 

  9. Comminges, L., Dalalyan, A.: Tight conditions for consistency of variable selection in the context of high dimensionality. Ann. Stat. 40, 2667–2696 (2012)

    Google Scholar 

  10. Cuevas, A.: A partial overview of the theory of statistics with functional data. J. Stat. Plann. Inference 147, 1–23 (2014)

    Google Scholar 

  11. Fan, J., Li, R.: Variable selection via nonconcave penalized likelihood and its oracle properties. J. Amer. Statist. Assoc. 96, 1348–1360 (2001)

    Google Scholar 

  12. Fan, J., Peng, H.: Nonconcave penalized likelihood with a diverging number of parameters. Ann. Stat. 32, 928–961 (2004)

    Google Scholar 

  13. Ferraty, F., Goia,A., Salinelli, E., Vieu, P.: Functional projection pursuit regression. Test 22, 293–320 (2013).

    Google Scholar 

  14. Ferraty, F., Hall, P., Vieu, P.: Most-predictive design points for functional data predictors. Biometrika 97, 807–824 (2010)

    Google Scholar 

  15. Ferraty, F., Vieu, P.: Nonparametric Functional Data Analysis. Springer-Verlag, New York (2006)

    Google Scholar 

  16. Goia, A., Vieu, P.: A partitioned single functional index model. Comput. Stat. 30, 673–692 (2015)

    Google Scholar 

  17. Goia, A., Vieu, P.: An introduction to recent advances in high/infinite dimensional statistics. J. Multivariate Anal. 46, 1–6 (2016)

    Google Scholar 

  18. Guo, J., Tang, M., Tian, M., Zhu, K.: Variable selection in high-dimensional partially linear additive models for composite quantile regression. Comput. Statist. Data Anal. 65, 56–67 (2013)

    Google Scholar 

  19. Härdle, W., Simar, L.: Applied Multivariate Statistical Analysis. (Fourth edition) Springer, Heidelberg (2015)

    Google Scholar 

  20. Hong, Z., Hu, Y., Lian, H.: Variable selection for high-dimensional varying coefficient partially linear models via nonconcave penalty. Metrika 76, 887–908 (2013)

    Google Scholar 

  21. Horváth, L., Kokoszka, P.: Inference for Functional Data with Applications. Springer, New York (2012)

    Google Scholar 

  22. Hsing, T., Eubank, R.: Theoretical Foundations of Functional Data Analysis, with an Introduction to Linear Operators. John Wiley & Sons, Chichester (2015)

    Google Scholar 

  23. Hu, Y., Lian, H.: Variable selection in a partially linear proportional hazards model with a diverging dimensionality. Stat. Probab. Lett. 83, 61–69 (2013)

    Google Scholar 

  24. Huang, J., Horowitz, J., Wei, F.: Variable selection in nonparametric additive models. Ann. Stat. 38, 2282–2313 (2010)

    Google Scholar 

  25. Huang, J., Xie, H.: Asymptotic oracle properties of SCAD-penalized least squared estimators. Asymptotics: Particles, Processes and Inverse Problems. In: IMS Lecture Notes-Monograph Series 55, 149–166 (2007)

    Google Scholar 

  26. Kneip, A., Poss, D., Sarda, P.: Functional linear regression with points of impact. Ann. Stat. 44, 1–30 (2016)

    Google Scholar 

  27. Kneip, A., Sarda, P.: Factor models and variable selection in high-dimensional regression analysis. Ann. Stat. 39, 2410–2447 (2011)

    Google Scholar 

  28. Lafferty, J.,Wasserman, L.: RODEO: Sparse, greedy, nonparametric regression. Ann. Stat. 36, 28–63 (2008)

    Google Scholar 

  29. Liu, S., McGree, J., Ge, Z., Xie, Y.: Computational and Statistical Methods for Analysing Big Data with Applications. Elsevier/Academic Press, Amsterdam (2015)

    Google Scholar 

  30. Matwin, S., Mielniczuk, J. (Eds): Challenges in Computational Statistics and Data Mining. Springer (2016)

    Google Scholar 

  31. McKeague, I., Sen, B.: Fractals with point impact in functional linear regression. Ann. Stat. 38, 2559–2586 (2010)

    Google Scholar 

  32. Meier, L., van de Geer, S., Bühlmann, P.: High-dimensional additive modeling. Ann. Stat. 37, 3779–3821 (2009)

    Google Scholar 

  33. Ramsay, J., Silverman, B.: Functional Data Analysis. (Second edition) Springer, New York (2005)

    Google Scholar 

  34. Vieu, P.: Choice of regressors in nonparametric estimation. Comput. Statist. Data Anal. 17, 575–594 (1994)

    Google Scholar 

  35. Wang, S., Su, L.: Simultaneous Lasso and Dantzig selector in high dimensional nonparametric regression. Int. J. Appl. Math. Stat. 42, 103–118 (2013)

    Google Scholar 

  36. Zhang, P.: Variable selection in nonparametric regression with continuous covariates. Ann. Stat. 19, 1869–1882 (1991)

    Google Scholar 

  37. Zhao, Y., Todd O., Reiss, P.: Wavelet-based LASSO in functional linear regression. J. Comput. Graph. Statist. 21, 600–617 (2012)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Departamento de Matemáticas, Universidade da Coruña, A Coruña, Spain

    Germán Aneiros

  2. Institut de Mathématiques, Université Paul Sabatier, Toulouse, France

    Philippe Vieu

Authors
  1. Germán Aneiros
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Philippe Vieu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Philippe Vieu .

Editor information

Editors and Affiliations

  1. Dept. of Mathematics, University of A Coruña, A Coruña, Spain

    Germán Aneiros

  2. Dept. of Studies in Econ.and Business, University of Eastern Piedmont "Amedeo Avogadro", Novara, Italy

    Enea G. Bongiorno

  3. Dept. of Mathematics, University of A Coruña, A Coruña, Spain

    Ricardo Cao

  4. Toulouse Mathematics Institute (IMT), Paul Sabatier University, Toulouse, France

    Philippe Vieu

Rights and permissions

Reprints and permissions

Copyright information

© 2017 Springer International Publishing AG

About this paper

Cite this paper

Aneiros, G., Vieu, P. (2017). A general sparse modeling approach for regression problems involving functional data. In: Aneiros, G., G. Bongiorno, E., Cao, R., Vieu, P. (eds) Functional Statistics and Related Fields. Contributions to Statistics. Springer, Cham. https://doi.org/10.1007/978-3-319-55846-2_5

Download citation

Publish with us

Policies and ethics

Search

Navigation