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The Dantzig Discriminant Analysis with High Dimensional Data

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  • Yanli Zhang
  • Lei Huo
  • Lu Lin
  • Yunhui Zeng

Abstract

It is well known that linear discriminant analysis (LDA) works well and is asymptotically optimal under fixed-p-large-n situations. But Bickel and Levina (2004) showed that the LDA is as bad as random guessing when p > n. This article studies the sparse discriminant analysis via Dantzig penalized least squares. Our method avoids estimating the high-dimensional covariance matrix and does not need the sparsity assumption on the inverse of the covariance matrix. We show that the new discriminant analysis is asymptotically optimal theoretically. Simulation and real data studies show that the classifier performs better than the existing sparse methods.

Suggested Citation

  • Yanli Zhang & Lei Huo & Lu Lin & Yunhui Zeng, 2014. "The Dantzig Discriminant Analysis with High Dimensional Data," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 43(23), pages 5012-5025, December.
    • Handle: RePEc:taf:lstaxx:v:43:y:2014:i:23:p:5012-5025
    DOI: 10.1080/03610926.2013.878359
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