Can One Decide the Type of the Mean from the Empirical Measure?

Abstract

The problem of deciding whether the mean of an unknown distribution is in a set Alpha or in its complement based on a sequence of independent random variables drawn according to this distribution is considered. Using large deviations techniques, an algorithm is proposed which is shown to lead to an a.s. correct decision for a class of Alpha which are necessarily countable. A refined decision procedure is also presented which, given a countable decomposition of Alpha, can determine a.s. to which set of the decomposition the mean belongs. This extends and simplifies a construction by Cover.

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Document Details

Document Type
Technical Report
Publication Date
Apr 01, 1990
Accession Number
ADA459509

Entities

People

  • Ofer Zeitouni
  • Sanjeev R. Kulkarni

Organizations

  • Massachusetts Institute of Technology

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  • Human Systems

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Fields of Study

  • Mathematics

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