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Sensitivity analysis in functional principal component analysis

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Summary

In the present paper empirical influence functions (EIFs) are derived for eigenvalues and eigenfunctions in functional principal component analysis in both cases where the smoothing parameter is fixed and unfixed. Based on the derived influence functions a sensitivity analysis procedure is proposed for detecting jointly as well as singly influential observations. A numerical example is given to show the usefulness of the proposed procedure. In dealing with the influence on the eigenfunctions two different kinds of influence statistics are introduced. One is based on the EIF for the coefficient vectors of the basis function expansion, and the other is based on the sampled vectors of the functional EIF. Under a certain condition it can be proved both kinds of statistics provide essentially equivalent results.

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Authors and Affiliations

  1. Bioinformatics Center, Institute for Chemical Research, Kyoto University, Gokasho, Uji, 611-0011, Kyoto, Japan

    Yoshihiro Yamanishi

  2. Department of Environmental and Mathematical Sciences, Okayama University, 3-1-1 Tsushima-Naka, Okayama, 700-8530, Okayama, Japan

    Yutaka Tanaka

Authors
  1. Yoshihiro Yamanishi
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  2. Yutaka Tanaka
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Yamanishi, Y., Tanaka, Y. Sensitivity analysis in functional principal component analysis. Computational Statistics 20, 311–326 (2005). https://doi.org/10.1007/BF02789706

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