Inequalities for the L1 Deviation of the Empirical Distribution

[摘要] 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. 10 Pages

[发布机构] HP Development Company

[学科分类] 计算机科学（综合）

[关键词] Sanov's theorem;Pinsker's inequality;large deviations;L(subscript 1) distance;divergence;variational distance;Chernoff bound