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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Testing Statistical Hypotheses Volume I

ISBN: 9783030705770

4th Edition

Authors: E.L. Lehmann, Joseph P. Romano

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