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Inequalities for the L1 Deviation of the Empirical Distribution

Weissman, Tsachy; Ordentlich, Erik; Seroussi, Gadiel; Verdu, Sergio; Weinberger, Marcelo J.

HPL-2003-97R1

Keyword(s): Sanov's theorem; Pinsker's inequality; large deviations; L(subscript 1) distance; divergence; variational distance; Chernoff bound

Abstract: We derive bounds on the probability that the L(subscript 1) distance between the empirical distribution of a sequence of independent identically distributed random variables and the true distribution is more than a specified value. We also derive a generalization of Pinsker's inequality relating the L(subscript 1) distance to the divergence.

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