Skip to main content
SpringerLink
Log in

Functional quantile regression: local linear modelisation

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

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

Abstract

A nonparametric local linear estimator of the conditional quantiles of a scalar response variable Y given a random variable X taking values in a semi-metric space. We establish the almost complete consistency and the asymptotic normality of this estimate. We prove that the asymptotic proprieties of this estimate are closely related to some topological characteristics of the data. Finally, a Monte Carlo study is carried out to evaluate the performance of this estimate.

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. Barrientos-Marin, J., Ferraty, F., Vieu, P.: Locally modelled regression and functional data. J. Nonparametr. Stat., 22, No. 5, 617–632 (2010)

    Google Scholar 

  2. Berlinet, A., Elamine, A., Mas, A.: Local linear regression for functional data. Ann. Inst. Statist. Math., 63, 1047–1075 (2011)

    Google Scholar 

  3. Baíllo, A., Grané, A.: Local linear regression for functional predictor and scalar response. J. Multivariate Anal., 100, 102–111 (2009)

    Google Scholar 

  4. Cardot, H.; Crambes, Ch., Sarda, P.: Quantile regression when the covariates are functions. J. Nonparametr. Stat., 17, 841–856 (2005)

    Google Scholar 

  5. Dabo-Niang, S., Kaid, Z., Laksaci, A.: Asymptotic properties of the kernel estimate of spatial conditional mode when the regressor is functional. AStA Adv. Stat. Anal. 99, 131–160 (2015)

    Google Scholar 

  6. Dabo-Niang, S., Laksaci, A.: Nonparametric quantile regression estimation for functional dependent data. Comm. Statist. Theory Methods, 41, 1254–1268 (2015)

    Google Scholar 

  7. Demongeot, J., Laksaci, A., Madani, F., Rachdi, M.: Functional data: local linear estimation of the conditional density and its application. Statistics, 47, 26–44 (2013)

    Google Scholar 

  8. Demongeot, J., Laksaci, A., Rachdi, M., Rahmaani S.: On the local linear modelization of the conditional distribution for functional data, Sankhya A 76 328–355 (2014)

    Google Scholar 

  9. Fan, J., Gijbels, I. Local polynomial modelling and its applications. London, Chapman & Hall (1996)

    Google Scholar 

  10. Ferraty, F., Vieu, P. Nonparametric functional data analysis. Theory and Practice. Springer Series in Statistics. New York (2006)

    Google Scholar 

  11. Goia, A., Vieu, P.: An introduction to recent advances in high/infinite dimensional Statistics. J. Multivariate Anal., 146, 1–6 (2016)

    Google Scholar 

  12. Hallin, M., Lu, Z., Yu, K.: Local linear spatial quantile regression. Bernoulli, 15, 659–686 (2009)

    Google Scholar 

  13. Hsing, T., Eubank, R.: Theoretical foundations of functional data analysis, with an introduction to linear operators. Wiley Series in Probability and Statistics. John Wiley & Sons, Chichester (2015)

    Google Scholar 

  14. Kato, K.: Estimation in functional linear quantile regression. Ann. Statist. 40, 3108–3136 (2012)

    Google Scholar 

  15. Laksaci, A., Lemdani, M., Ould Saïd, E.: A generalized L 1-approach for a kernel estimator of conditional quantile with functional regressors: Consistency and asymptotic normality. Statist. Probab. Lett., 79, 1065–1073 (2009)

    Google Scholar 

  16. Messaci, F., Nemouchi, N., Ouassou, I., Rachdi, M.: Local polynomial modelling of the conditional quantile for functional data. Stat. Methods Appl. 24, 597–622 (2015)

    Google Scholar 

  17. Ramsay, J.O., Silverman, B.W.: Applied functional data analysis. Methods and case studies. Springer Series in Statistics. New York (2002)

    Google Scholar 

  18. Samanta, M.: Non-parametric estimation of conditional quantiles. Statist. Probab. Lett., 7, 407–412 (1989)

    Google Scholar 

  19. Stone, C.J.: Consistent nonparametric regression. Discussion. Ann. Statist., 5, 595–645 (1977)

    Google Scholar 

  20. Wang, K., Lin, L.: Variable selection in semiparametric quantile modeling for longitudinal data. Comm. Statist. Theory Methods 44, 2243–2266, (2015)

    Google Scholar 

  21. Zhang, J.: Analysis of variance for functional data. Monographs on Statistics and Applied Probability, 127. CRC Press, Boca Raton, FL (2014)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Laboratoire de Statistique et Processus Stochastiques, Université Djillali Liabès, BP. 89, 22000, Sidi Bel-Abbès, Algeria

    Zoulikha Kaid & Ali Laksaci

Authors
  1. Zoulikha Kaid
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ali Laksaci
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ali Laksaci .

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

Kaid, Z., Laksaci, A. (2017). Functional quantile regression: local linear modelisation. 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_20

Download citation

Publish with us

Policies and ethics

Search

Navigation