Fast rate of convergence in high-dimensional linear discriminant analysis

R. Girard

Journal of Nonparametric Statistics, 2011, vol. 23, issue 1, 165-183

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.

Date: 2011
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DOI: 10.1080/10485252.2010.487531

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