Toward fast rate of convergence in high dimensional linear discriminant analysis

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.