INADMISSIBILITY OF THE BEST INVARIANT TEST WHEN THE MOMENT IS INFINITE UNDER ONE OF THE HYPOTHESES.
Technical summary rept.,
WISCONSIN UNIV MADISON MATHEMATICS RESEARCH CENTER
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Let X and Y be real valued random variables with joint density g sub i y f sub i x-theta, y under the hypothesis H sub i i 1, 2. Assume theta is unknown. The best invariant test of H sub 1 vs H sub 2 is known to be admissible if X has a finite first moment under both hypotheses. The present paper provides an example in which admissibility fails if under one hypothesis the first moment is infinite. Author
- Statistics and Probability