Can one decide the type of the mean from the empirical measure?

Sanjeev R. Kulkarni, Ofer Zeitouni

Research output: Contribution to journalArticlepeer-review

5 Scopus citations


The problem of deciding whether the mean of an unknown distribution is in a set A or in its complement based on a sequence of independent random variables drawn according to this distribution is considered. We propose an algorithm which leads to an a.s. correct decision for any A in a class of sets satisfying certain structural assumptions. This class includes not only all countable sets, but many uncountable sets as well. A refined decision procedure is also presented which, given a countable decomposition of A, can determine a.s. to which set of the decomposition the mean belongs. This extends and simplifies a construction by Cover.

Original languageEnglish (US)
Pages (from-to)323-327
Number of pages5
JournalStatistics and Probability Letters
Issue number4
StatePublished - Oct 1991
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


  • Cramer's theorem
  • Hypothesis testing
  • empirical measure


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