INADMISSIBILITY OF THE BEST INVARIANT TEST WHEN THE MOMENT IS INFINITE UNDER ONE OF THE HYPOTHESES
Abstract : 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)