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Fast rate of convergence in high-dimensional linear discriminant analysis

Robin Girard 1
1 CEP/Sophia
CEP - Centre Énergétique et Procédés
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.
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Submitted on : Wednesday, July 28, 2010 - 11:10:04 AM
Last modification on : Thursday, September 24, 2020 - 5:22:02 PM

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

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