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On prediction error in functional linear regression

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  • Apanasovich, Tatiyana V.
  • Goldstein, Edward

Abstract

We consider a regression setting where the response is a scalar and the predictor is a random function. Many fields of applications are concerned with such data, for example chemometrics. When researchers are faced with the estimation of a functional (infinite dimensional) coefficient, they reduce the dimension by projecting the weight function onto a lower dimensional space. We derive an upper bound for the mean squared error of prediction when the choice of the lower dimensional space is guided by the smoothness of the regression function.

Suggested Citation

  • Apanasovich, Tatiyana V. & Goldstein, Edward, 2008. "On prediction error in functional linear regression," Statistics & Probability Letters, Elsevier, vol. 78(13), pages 1807-1810, September.
    • Handle: RePEc:eee:stapro:v:78:y:2008:i:13:p:1807-1810
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    References listed on IDEAS

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    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. 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.
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    Cited by:

    1. Peter Hall & Giles Hooker, 2016. "Truncated linear models for functional data," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 78(3), pages 637-653, June.
    2. A. Delaigle & P. Hall, 2016. "Approximating fragmented functional data by segments of Markov chains," Biometrika, Biometrika Trust, vol. 103(4), pages 779-799.
    3. Shin, Hyejin & Lee, Myung Hee, 2012. "On prediction rate in partial functional linear regression," Journal of Multivariate Analysis, Elsevier, vol. 103(1), pages 93-106, January.

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