IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v101y2010i2p327-339.html
   My bibliography  Save this article

Measures of influence for the functional linear model with scalar response

Author

Listed:
  • Febrero-Bande, Manuel
  • Galeano, Pedro
  • González-Manteiga, Wenceslao

Abstract

This paper studies how to identify influential observations in the functional linear model in which the predictor is functional and the response is scalar. Measurement of the effects of a single observation on estimation and prediction when the model is estimated by the principal components method is undertaken. For that, three statistics are introduced for measuring the influence of each observation on estimation and prediction of the functional linear model with scalar response that are generalizations of the measures proposed for the standard regression model by [D.R. Cook, Detection of influential observations in linear regression, Technometrics 19 (1977) 15-18; D. Peña, A new statistic for influence in linear regression, Technometrics 47 (2005) 1-12] respectively. A smoothed bootstrap method is proposed to estimate the quantiles of the influence measures, which allows us to point out which observations have the larger influence on estimation and prediction. The behavior of the three statistics and the quantile estimation bootstrap based method is analyzed via a simulation study. Finally, the practical use of the proposed statistics is illustrated by the analysis of a real data example, which show that the proposed measures are useful for detecting heterogeneity in the functional linear model with scalar response.

Suggested Citation

  • Febrero-Bande, Manuel & Galeano, Pedro & González-Manteiga, Wenceslao, 2010. "Measures of influence for the functional linear model with scalar response," Journal of Multivariate Analysis, Elsevier, vol. 101(2), pages 327-339, February.
    • Handle: RePEc:eee:jmvana:v:101:y:2010:i:2:p:327-339
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047-259X(08)00276-5
    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. Chiou, Jeng-Min & Muller, Hans-Georg, 2007. "Diagnostics for functional regression via residual processes," Computational Statistics & Data Analysis, Elsevier, vol. 51(10), pages 4849-4863, June.
    2. Cardot, Hervé & Ferraty, Frédéric & Sarda, Pascal, 1999. "Functional linear model," Statistics & Probability Letters, Elsevier, vol. 45(1), pages 11-22, October.
    3. 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.
    4. Svitlana Tyekucheva & Francesca Chiaromonte, 2008. "Rejoinder on: Augmenting the bootstrap to analyze high dimensional genomic data," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 17(1), pages 47-55, May.
    5. Cuevas, Antonio & Febrero, Manuel & Fraiman, Ricardo, 2006. "On the use of the bootstrap for estimating functions with functional data," Computational Statistics & Data Analysis, Elsevier, vol. 51(2), pages 1063-1074, November.
    6. Bing Li, 2008. "Comments on: Augmenting the bootstrap to analyze high dimensional genomic data," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 17(1), pages 19-21, May.
    7. Peter Hall & Mohammad Hosseini‐Nasab, 2006. "On properties of functional principal components analysis," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(1), pages 109-126, February.
    8. Svitlana Tyekucheva & Francesca Chiaromonte, 2008. "Augmenting the bootstrap to analyze high dimensional genomic data," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 17(1), pages 1-18, May.
    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. Febrero-Bande, Manuel & de la Fuente, Manuel Oviedo, 2012. "Statistical Computing in Functional Data Analysis: The R Package fda.usc," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 51(i04).
    2. Siegfried Hörmann & Łukasz Kidziński, 2015. "A Note on Estimation in Hilbertian Linear Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 42(1), pages 43-62, March.
    3. 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.

    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. 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.
    2. 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.
    3. Delsol, Laurent & Ferraty, Frédéric & Vieu, Philippe, 2011. "Structural test in regression on functional variables," Journal of Multivariate Analysis, Elsevier, vol. 102(3), pages 422-447, March.
    4. 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.
    5. 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.
    6. 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.
    7. Han Shang, 2014. "A survey of functional principal component analysis," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 98(2), pages 121-142, April.
    8. Siegfried Hörmann & Łukasz Kidziński & Piotr Kokoszka, 2015. "Estimation in Functional Lagged Regression," Journal of Time Series Analysis, Wiley Blackwell, vol. 36(4), pages 541-561, July.
    9. Yue Wang & Joseph G. Ibrahim & Hongtu Zhu, 2020. "Partial least squares for functional joint models with applications to the Alzheimer's disease neuroimaging initiative study," Biometrics, The International Biometric Society, vol. 76(4), pages 1109-1119, December.
    10. 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.
    11. Dehan Kong & Joseph G. Ibrahim & Eunjee Lee & Hongtu Zhu, 2018. "FLCRM: Functional linear cox regression model," Biometrics, The International Biometric Society, vol. 74(1), pages 109-117, March.
    12. 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.
    13. Frédéric Ferraty & Ingrid Van Keilegom & Philippe Vieu, 2010. "On the Validity of the Bootstrap in Non‐Parametric Functional Regression," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 37(2), pages 286-306, June.
    14. Lakraj, Gamage Pemantha & Ruymgaart, Frits, 2017. "Some asymptotic theory for Silverman’s smoothed functional principal components in an abstract Hilbert space," Journal of Multivariate Analysis, Elsevier, vol. 155(C), pages 122-132.
    15. 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.
    16. 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.
    17. Kehui Chen & Xiaoke Zhang & Alexander Petersen & Hans-Georg Müller, 2017. "Quantifying Infinite-Dimensional Data: Functional Data Analysis in Action," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 9(2), pages 582-604, December.
    18. 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.
    19. Philip T. Reiss & Jeff Goldsmith & Han Lin Shang & R. Todd Ogden, 2017. "Methods for Scalar-on-Function Regression," International Statistical Review, International Statistical Institute, vol. 85(2), pages 228-249, August.
    20. Cardot, Hervé & Sarda, Pacal, 2005. "Estimation in generalized linear models for functional data via penalized likelihood," Journal of Multivariate Analysis, Elsevier, vol. 92(1), pages 24-41, January.

    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:327-339. 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.