IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v113y2016icp7-15.html
   My bibliography  Save this article

Estimation of the noise covariance operator in functional linear regression with functional outputs

Author

Listed:
  • Crambes, Christophe
  • Hilgert, Nadine
  • Manrique, Tito

Abstract

This work deals with the estimation of the noise in functional linear regression when both the response and the covariate are functional. Namely, we propose two estimators of the covariance operator of the noise. We give some asymptotic properties of these estimators, and we study their behavior on simulations.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:113:y:2016:i:c:p:7-15
    DOI: 10.1016/j.spl.2016.02.006
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167715216000353
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spl.2016.02.006?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.
    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. Amel, Azzi & Ali, Laksaci & Elias, Ould Saïd, 2022. "On the robustification of the kernel estimator of the functional modal regression," Statistics & Probability Letters, Elsevier, vol. 181(C).

    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. 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.
    2. 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.
    3. 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).
    4. 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.
    5. 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.
    6. Yu, Dengdeng & Zhang, Li & Mizera, Ivan & Jiang, Bei & Kong, Linglong, 2019. "Sparse wavelet estimation in quantile regression with multiple functional predictors," Computational Statistics & Data Analysis, Elsevier, vol. 136(C), pages 12-29.
    7. Laurent Delsol, 2013. "No effect tests in regression on functional variable and some applications to spectrometric studies," Computational Statistics, Springer, vol. 28(4), pages 1775-1811, August.
    8. Shuzhi Zhu & Peixin Zhao, 2019. "Tests for the linear hypothesis in semi-functional partial linear regression models," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 82(2), pages 125-148, March.
    9. Manuel Febrero-Bande & Pedro Galeano & Wenceslao González-Manteiga, 2017. "Functional Principal Component Regression and Functional Partial Least-squares Regression: An Overview and a Comparative Study," International Statistical Review, International Statistical Institute, vol. 85(1), pages 61-83, April.
    10. Shuang Wu & Hans-Georg Müller, 2011. "Response-Adaptive Regression for Longitudinal Data," Biometrics, The International Biometric Society, vol. 67(3), pages 852-860, September.
    11. Eduardo García‐Portugués & Javier Álvarez‐Liébana & Gonzalo Álvarez‐Pérez & Wenceslao González‐Manteiga, 2021. "A goodness‐of‐fit test for the functional linear model with functional response," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 48(2), pages 502-528, June.
    12. Fabrizio Maturo & Antonio Balzanella & Tonio Di Battista, 2019. "Building Statistical Indicators of Equitable and Sustainable Well-Being in a Functional Framework," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 146(3), pages 449-471, December.
    13. Cuevas, Antonio & Febrero, Manuel & Fraiman, Ricardo, 2004. "An anova test for functional data," Computational Statistics & Data Analysis, Elsevier, vol. 47(1), pages 111-122, August.
    14. Maria Grith & Wolfgang K. Härdle & Alois Kneip & Heiko Wagner, 2016. "Functional Principal Component Analysis for Derivatives of Multivariate Curves," SFB 649 Discussion Papers SFB649DP2016-033, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    15. Said Attaoui & Nengxiang Ling, 2016. "Asymptotic results of a nonparametric conditional cumulative distribution estimator in the single functional index modeling for time series data with applications," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 79(5), pages 485-511, July.
    16. Guillas, Serge, 2001. "Rates of convergence of autocorrelation estimates for autoregressive Hilbertian processes," Statistics & Probability Letters, Elsevier, vol. 55(3), pages 281-291, December.
    17. Ping Yu & Zhongzhan Zhang & Jiang Du, 2016. "A test of linearity in partial functional linear regression," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 79(8), pages 953-969, November.
    18. Qi, Xin & Luo, Ruiyan, 2018. "Function-on-function regression with thousands of predictive curves," Journal of Multivariate Analysis, Elsevier, vol. 163(C), pages 51-66.
    19. Ferraty, F. & Vieu, P., 2003. "Curves discrimination: a nonparametric functional approach," Computational Statistics & Data Analysis, Elsevier, vol. 44(1-2), pages 161-173, October.
    20. Valencia García, Dalia Jazmin & Lillo Rodríguez, Rosa Elvira & Romo, Juan, 2013. "A Kendall correlation coefficient for functional dependence," DES - Working Papers. Statistics and Econometrics. WS ws133228, Universidad Carlos III de Madrid. Departamento de Estadística.

    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:stapro:v:113:y:2016:i:c:p:7-15. 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: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    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.