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Most-predictive design points for functional data predictors

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  • F. Ferraty
  • P. Hall
  • P. Vieu
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    Abstract

    We suggest a way of reducing the very high dimension of a functional predictor, X, to a low number of dimensions chosen so as to give the best predictive performance. Specifically, if X is observed on a fine grid of design points t 1,…, t r, we propose a method for choosing a small subset of these, say t i1 ,…, t ik , to optimize the prediction of a response variable, Y. The values t ij are referred to as the most predictive design points, or covariates, for a given value of k, and are computed using information contained in a set of independent observations (X i, Y i) of (X, Y). The algorithm is based on local linear regression, and calculations can be accelerated using linear regression to preselect the design points. Boosting can be employed to further improve the predictive performance. We illustrate the usefulness of our ideas through simulations and examples drawn from chemometrics, and we develop theoretical arguments showing that the methodology can be applied successfully in a range of settings. Copyright 2010, Oxford University Press.

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    File URL: http://hdl.handle.net/10.1093/biomet/asq058
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    Bibliographic Info

    Article provided by Biometrika Trust in its journal Biometrika.

    Volume (Year): 97 (2010)
    Issue (Month): 4 ()
    Pages: 807-824

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    Handle: RePEc:oup:biomet:v:97:y:2010:i:4:p:807-824

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    Postal: Oxford University Press, Great Clarendon Street, Oxford OX2 6DP, UK
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    Cited by:
    1. Matsui, Hidetoshi & Konishi, Sadanori, 2011. "Variable selection for functional regression models via the L1 regularization," Computational Statistics & Data Analysis, Elsevier, vol. 55(12), pages 3304-3310, December.
    2. Zhang, Tao & Zhang, Qingzhao & Wang, Qihua, 2014. "Model detection for functional polynomial regression," Computational Statistics & Data Analysis, Elsevier, vol. 70(C), pages 183-197.
    3. Diego Vidaurre & Concha Bielza & Pedro Larrañaga, 2012. "Lazy lasso for local regression," Computational Statistics, Springer, vol. 27(3), pages 531-550, September.

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