On the Convergence of the Empirical Distribution

Daniel Berend; Aryeh Kontorovich

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arXiv · 1205.6711

On the Convergence of the Empirical Distribution

Daniel Berend·Aryeh Kontorovich

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Abstract

We develop a general technique for bounding the tail of the total variation distance between the empirical and the true distributions over countable sets. Our methods sharpen a deviation bound of Devroye (1983) for distributions over finite sets, and also hold for the broader class of distributions with countable support. We also provide some lower bounds of possible independent interest.

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Daniel Berend, Aryeh Kontorovich. 2012-06-05. On the Convergence of the Empirical Distribution. https://arxiv.org/abs/1205.6711

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