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Inequalities for the L1 Deviation of the Empirical Distribution
Weissman, Tsachy; Ordentlich, Erik; Seroussi, Gadiel; Verdu, Sergio; Weinberger, Marcelo J.
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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