Under the assumptions of Theorem9.4.1, suppose there exists another monotone rule E that strongly controls the FWER,

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Under the assumptions of Theorem9.4.1, suppose there exists another monotone rule E that strongly controls the FWER, and such that Pθ{dc 0,0} ≤ Pθ{ec 0,0} for all θ ∈ ωc 0,0 , (9.143)

with strict inequality for some θ ∈ ωc 0,0. Argue that the ≤ in (9.143) is an equality, and hence e0,0d0,0 has Lebesgue measure 0, where AB denotes the symmetric difference between sets A and B. A similar result for the region d1,1 can be made as well.

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Testing Statistical Hypotheses Volume I

ISBN: 9783030705770

4th Edition

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

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