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

Author

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  • Kulkarni, Sanjeev R.
  • Zeitouni, Ofer

Abstract

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.

Suggested Citation

  • Kulkarni, Sanjeev R. & Zeitouni, Ofer, 1991. "Can one decide the type of the mean from the empirical measure?," Statistics & Probability Letters, Elsevier, vol. 12(4), pages 323-327, October.
    • Handle: RePEc:eee:stapro:v:12:y:1991:i:4:p:323-327
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