LetX1,...,Xm andYt,...,Y be independent, random samples from populations which are N(θ,σx2) and N(θ,σy2), respectively, with all parameters unknown. In testingH0:θ=0 againstH1:θ≠0, thet-test based upon either sample is known to be admissible in the two-sample setting. If, however, one testsH0 againstH1:|θ|≧ε>0, with ε arbitrary, our main results show: (i) the construction of a test which is better than the particulart-test chosen, (ii) eacht-test is admissible under the invariance principle with respect to the group of scale changes, and (iii) there does not exist a test which simultaneously is better than botht-tests.
AMS 1970 subject classifications
Primary 62F05 Secondary 62A06 62C15
Key words and phrases
Common mean indifference zone t-test invariance
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