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Fast rate of convergence in high-dimensional linear discriminant analysis

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  • R. Girard

Abstract

This paper gives a theoretical analysis of high-dimensional linear discrimination of Gaussian data. We study the excess risk of linear discriminant rules. We emphasis the poor performances of standard procedures in the case when dimension p is larger than sample size n. The corresponding theoretical results are non-asymptotic lower bounds. On the other hand, we propose two discrimination procedures based on dimensionality reduction and provide associated rates of convergence which can be O(log(p)/n) under sparsity assumptions. Finally, all our results rely on a theorem that provides simple sharp relations between the excess risk and an estimation error associated with the geometric parameters defining the used discrimination rule.

Suggested Citation

  • R. Girard, 2011. "Fast rate of convergence in high-dimensional linear discriminant analysis," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 23(1), pages 165-183.
  • Handle: RePEc:taf:gnstxx:v:23:y:2011:i:1:p:165-183
    DOI: 10.1080/10485252.2010.487531
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