To generalize the results of the preceding problem to the testing of H : f versus K
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To generalize the results of the preceding problem to the testing of H : f versus K : { fθ , θ ∈ ω}, assume:
(i) There exists a group G that leaves H and K invariant.
(ii) G¯ is transitive over ω.
(iii) There exists a probability distribution Q over G which is right invariant in the sense of Section 8.4.
Determine a UMP invariant test, and show that it is both maximin against K and admissible.
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Related Book For
Testing Statistical Hypotheses Volume I
ISBN: 9783030705770
4th Edition
Authors: E.L. Lehmann, Joseph P. Romano
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