Bias-Corrected Diagonal Discriminant Rules for High-Dimensional Classification

Authors

  • Song Huang,

    Corresponding author
    1. Program of Computational Biology and Bioinformatics, Yale University, New Haven, Connecticut 06520, U.S.A.
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  • Tiejun Tong,

    Corresponding author
    1. Department of Applied Mathematics, University of Colorado, Boulder, Colorado 80309, U.S.A.
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  • Hongyu Zhao

    Corresponding author
    1. Department of Epidemiology and Public Health, Yale University, New Haven, Connecticut 06520, U.S.A.
    2. Department of Genetics, Yale University, New Haven, Connecticut 06520, U.S.A.
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email:song.huang@yale.edu

email:tiejun.tong@colorado.edu

email:hongyu.zhao@yale.edu

Abstract

Summary Diagonal discriminant rules have been successfully used for high-dimensional classification problems, but suffer from the serious drawback of biased discriminant scores. In this article, we propose improved diagonal discriminant rules with bias-corrected discriminant scores for high-dimensional classification. We show that the proposed discriminant scores dominate the standard ones under the quadratic loss function. Analytical results on why the bias-corrected rules can potentially improve the predication accuracy are also provided. Finally, we demonstrate the improvement of the proposed rules over the original ones through extensive simulation studies and real case studies.

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