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Article Dans Une Revue Journal of Nonparametric Statistics Année : 2011

Fast rate of convergence in high-dimensional linear discriminant analysis

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Robin Girard

Résumé

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.

Dates et versions

hal-00506556 , version 1 (28-07-2010)

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Robin Girard. Fast rate of convergence in high-dimensional linear discriminant analysis. Journal of Nonparametric Statistics, 2011, 23 (1), pp.Pages 165-183. ⟨10.1080/10485252.2010.487531⟩. ⟨hal-00506556⟩
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