Abstract: | Summary LetX
1,...,X
m andY
t,...,Y be independent, random samples from populations which are N(θ,σ
x
2
) and N(θ,σ
y
2
), respectively, with all parameters unknown. In testingH
0:θ=0 againstH
1:θ≠0, thet-test based upon either sample is known to be admissible in the two-sample setting. If, however, one testsH
0 againstH
1:|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. |