IDEAS home Printed from https://ideas.repec.org/a/spr/compst/v17y2002i4d10.1007_s001800200126.html
   My bibliography  Save this article

The Functional Nonparametric Model and Application to Spectrometric Data

Author

Listed:
  • Frédéric Ferraty

    (Université Paul Sabatier
    Université Toulouse Le Mirail)

  • Philippe Vieu

    (Université Paul Sabatier)

Abstract

Summary The aim of this paper is to present a nonparametric regression model with scalar response when the explanatory variables are curves. In this context, the crucial problem of dimension reduction is overriden by the use of an implicit fractal dimension hypothesis. For such a functional nonparametric regression model we introduce and study both practical and theoretical aspects of some kernel type estimator. After a simulation study, it is shown how this procedure is well adapted to some spectrometric data set. Asymptotic results are described and in conclusion it turns out that this method combines advantages of easy implementation and good mathematical properties.

Suggested Citation

  • Frédéric Ferraty & Philippe Vieu, 2002. "The Functional Nonparametric Model and Application to Spectrometric Data," Computational Statistics, Springer, vol. 17(4), pages 545-564, December.
    • Handle: RePEc:spr:compst:v:17:y:2002:i:4:d:10.1007_s001800200126
    DOI: 10.1007/s001800200126
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s001800200126
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s001800200126?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. Cardot, Hervé & Ferraty, Frédéric & Sarda, Pascal, 1999. "Functional linear model," Statistics & Probability Letters, Elsevier, vol. 45(1), pages 11-22, October.
    2. Brown P.J. & Fearn T & Vannucci M, 2001. "Bayesian Wavelet Regression on Curves With Application to a Spectroscopic Calibration Problem," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 398-408, June.
    3. Vicente Núñez-Antón & Juan Rodríguez-Póo & Philippe Vieu, 1999. "Longitudinal data with nonstationary errors: a nonparametric three-stage approach," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 8(1), pages 201-231, June.
    4. M. C. Denham & P. J. Brown, 1993. "Calibration with Many Variables," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 42(3), pages 515-528, September.
    5. Besse, Philippe C. & Cardot, Herve & Ferraty, Frederic, 1997. "Simultaneous non-parametric regressions of unbalanced longitudinal data," Computational Statistics & Data Analysis, Elsevier, vol. 24(3), pages 255-270, May.
    Full references (including those not matched with items on IDEAS)

    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. Amato, U. & Antoniadis, A. & De Feis, I., 2006. "Dimension reduction in functional regression with applications," Computational Statistics & Data Analysis, Elsevier, vol. 50(9), pages 2422-2446, May.
    2. Luo, Ruiyan & Qi, Xin, 2015. "Sparse wavelet regression with multiple predictive curves," Journal of Multivariate Analysis, Elsevier, vol. 134(C), pages 33-49.
    3. Cao, Jiguo & Ramsay, James O., 2009. "Generalized profiling estimation for global and adaptive penalized spline smoothing," Computational Statistics & Data Analysis, Elsevier, vol. 53(7), pages 2550-2562, May.
    4. Febrero-Bande, Manuel & Galeano, Pedro & González-Manteiga, Wenceslao, 2019. "Estimation, imputation and prediction for the functional linear model with scalar response with responses missing at random," Computational Statistics & Data Analysis, Elsevier, vol. 131(C), pages 91-103.
    5. Qi, Xin & Zhao, Hongyu, 2011. "Some theoretical properties of Silverman's method for Smoothed functional principal component analysis," Journal of Multivariate Analysis, Elsevier, vol. 102(4), pages 741-767, April.
    6. Chakraborty, Sounak, 2012. "Bayesian multiple response kernel regression model for high dimensional data and its practical applications in near infrared spectroscopy," Computational Statistics & Data Analysis, Elsevier, vol. 56(9), pages 2742-2755.
    7. Hervé Cardot & Frédéric Ferraty & André Mas & Pascal Sarda, 2003. "Testing Hypotheses in the Functional Linear Model," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 30(1), pages 241-255, March.
    8. Comte , Fabienne & Johannes, Jan, 2011. "Adaptive functional linear regression," LIDAM Discussion Papers ISBA 2011038, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    9. González-Rodríguez, Gil & Colubi, Ana, 2017. "On the consistency of bootstrap methods in separable Hilbert spaces," Econometrics and Statistics, Elsevier, vol. 1(C), pages 118-127.
    10. Kalogridis, Ioannis & Van Aelst, Stefan, 2023. "Robust penalized estimators for functional linear regression," Journal of Multivariate Analysis, Elsevier, vol. 194(C).
    11. Amiri, Aboubacar & Crambes, Christophe & Thiam, Baba, 2014. "Recursive estimation of nonparametric regression with functional covariate," Computational Statistics & Data Analysis, Elsevier, vol. 69(C), pages 154-172.
    12. Hörmann, Siegfried & Jammoul, Fatima, 2023. "Prediction in functional regression with discretely observed and noisy covariates," Computational Statistics & Data Analysis, Elsevier, vol. 178(C).
    13. Geenens, Gery, 2015. "Moments, errors, asymptotic normality and large deviation principle in nonparametric functional regression," Statistics & Probability Letters, Elsevier, vol. 107(C), pages 369-377.
    14. Chakraborty, Sounak & Ghosh, Malay & Mallick, Bani K., 2012. "Bayesian nonlinear regression for large p small n problems," Journal of Multivariate Analysis, Elsevier, vol. 108(C), pages 28-40.
    15. 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.
    16. Dalia Valencia & Rosa E. Lillo & Juan Romo, 2019. "A Kendall correlation coefficient between functional data," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 13(4), pages 1083-1103, December.
    17. John A. Rice & Colin O. Wu, 2001. "Nonparametric Mixed Effects Models for Unequally Sampled Noisy Curves," Biometrics, The International Biometric Society, vol. 57(1), pages 253-259, March.
    18. Crambes, Christophe & Hilgert, Nadine & Manrique, Tito, 2016. "Estimation of the noise covariance operator in functional linear regression with functional outputs," Statistics & Probability Letters, Elsevier, vol. 113(C), pages 7-15.
    19. André Mas & Besnik Pumo, 2009. "Functional linear regression with derivatives," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 21(1), pages 19-40.
    20. André Mas, 2002. "Testing for the Mean of Random Curves : from Penalization to Dimension Selection," Working Papers 2002-08, Center for Research in Economics and Statistics.

    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:spr:compst:v:17:y:2002:i:4:d:10.1007_s001800200126. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.