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On prediction rate in partial functional linear regression

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  • Shin, Hyejin
  • Lee, Myung Hee
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    Abstract

    We consider a prediction of a scalar variable based on both a function-valued variable and a finite number of real-valued variables. For the estimation of the regression parameters, which include the infinite dimensional function as well as the slope parameters for the real-valued variables, it is inevitable to impose some kind of regularization. We consider two different approaches, which are shown to achieve the same convergence rate of the mean squared prediction error under respective assumptions. One is based on functional principal components regression (FPCR) and the alternative is functional ridge regression (FRR) based on Tikhonov regularization. Also, numerical studies are carried out for a simulation data and a real data.

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    Bibliographic Info

    Article provided by Elsevier in its journal Journal of Multivariate Analysis.

    Volume (Year): 103 (2012)
    Issue (Month): 1 (January)
    Pages: 93-106

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    Handle: RePEc:eee:jmvana:v:103:y:2012:i:1:p:93-106

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    Related research

    Keywords: Functional linear regression Mean squared prediction error Convergence rate Asymptotic normality;

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    1. Aneiros-Pérez, Germán & Vieu, Philippe, 2006. "Semi-functional partial linear regression," Statistics & Probability Letters, Elsevier, vol. 76(11), pages 1102-1110, June.
    2. Cardot, Hervé & Johannes, Jan, 2010. "Thresholding projection estimators in functional linear models," Journal of Multivariate Analysis, Elsevier, vol. 101(2), pages 395-408, February.
    3. Li, Yehua & Hsing, Tailen, 2007. "On rates of convergence in functional linear regression," Journal of Multivariate Analysis, Elsevier, vol. 98(9), pages 1782-1804, October.
    4. Apanasovich, Tatiyana V. & Goldstein, Edward, 2008. "On prediction error in functional linear regression," Statistics & Probability Letters, Elsevier, vol. 78(13), pages 1807-1810, September.
    5. Aneiros-Pérez, Germán & Vieu, Philippe, 2008. "Nonparametric time series prediction: A semi-functional partial linear modeling," Journal of Multivariate Analysis, Elsevier, vol. 99(5), pages 834-857, May.
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