IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v101y2010i2p476-490.html
   My bibliography  Save this article

Estimation of the regression operator from functional fixed-design with correlated errors

Author

Listed:
  • Benhenni, K.
  • Hedli-Griche, S.
  • Rachdi, M.

Abstract

We consider the estimation of the regression operator r in the functional model: Y=r(x)+[epsilon], where the explanatory variable x is of functional fixed-design type, the response Y is a real random variable and the error process [epsilon] is a second order stationary process. We construct the kernel type estimate of r from functional data curves and correlated errors. Then we study their performances in terms of the mean square convergence and the convergence in probability. In particular, we consider the cases of short and long range error processes. When the errors are negatively correlated or come from a short memory process, the asymptotic normality of this estimate is derived. Finally, some simulation studies are conducted for a fractional autoregressive integrated moving average and for an Ornstein-Uhlenbeck error processes.

Suggested Citation

  • Benhenni, K. & Hedli-Griche, S. & Rachdi, M., 2010. "Estimation of the regression operator from functional fixed-design with correlated errors," Journal of Multivariate Analysis, Elsevier, vol. 101(2), pages 476-490, February.
  • Handle: RePEc:eee:jmvana:v:101:y:2010:i:2:p:476-490
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047-259X(09)00184-5
    Download Restriction: Full text for ScienceDirect subscribers only

    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. Boente, Graciela & Fraiman, Ricardo, 2000. "Kernel-based functional principal components," Statistics & Probability Letters, Elsevier, vol. 48(4), pages 335-345, July.
    2. K. Benhenni & F. Ferraty & M. Rachdi & P. Vieu, 2007. "Local smoothing regression with functional data," Computational Statistics, Springer, vol. 22(3), pages 353-369, September.
    3. Benhenni, K. & Hedli-Griche, S. & Rachdi, M. & Vieu, P., 2008. "Consistency of the regression estimator with functional data under long memory conditions," Statistics & Probability Letters, Elsevier, vol. 78(8), pages 1043-1049, June.
    4. Roussas, George G., 2000. "Asymptotic normality of the kernel estimate of a probability density function under association," Statistics & Probability Letters, Elsevier, vol. 50(1), pages 1-12, October.
    5. Roussas, G. G., 1994. "Asymptotic Normality of Random Fields of Positively or Negatively Associated Processes," Journal of Multivariate Analysis, Elsevier, vol. 50(1), pages 152-173, July.
    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. Karim Benhenni & Sonia Hedli-Griche & Mustapha Rachdi, 2017. "Regression models with correlated errors based on functional random design," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 26(1), pages 1-21, March.
    2. Idir Ouassou & Mustapha Rachdi, 2012. "Regression operator estimation by delta-sequences method for functional data and its applications," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 96(4), pages 451-465, October.

    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:jmvana:v:101:y:2010:i:2:p:476-490. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Dana Niculescu). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    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 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.

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.