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

Sanjeev R. Kulkarni and Ofer Zeitouni

Statistics & Probability Letters, 1991, vol. 12, issue 4, 323-327

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.

Keywords: Hypothesis; testing; empirical; measure; Cramers; theorem (search for similar items in EconPapers)
Date: 1991
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