On the Convergence of the Empirical Distribution

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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.
Original languageEnglish GB
StatePublished - 2012

Publication series

NamearXiv PrePrint,

Keywords

  • math.ST
  • stat.TH
  • 62G07, 62G20

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