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Toward fast rate of convergence in high dimensional linear discriminant analysis

Abstract

This paper gives a theoretical analyze of high dimensional lin- ear discrimination of Gaussian data. We study the excess risk of a class of linear discriminant rules. Our main result allow us to give two types of sim- ple non asymptotic bounds: lower bounds associated to discrimination rules that fail in a high dimensional setting and upper bounds for for procedure that are adapted to the so called p >> n discrimination framework.

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