In general, the optimality results of Section 9.4 require the procedures to be monotone. To see why
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In general, the optimality results of Section 9.4 require the procedures to be monotone. To see why this is required, consider Theorem 9.4.2(i). Show the procedure E to be inadmissible. Hint: One can always add large negative values of T1 and T2 to the region u1,1 without violating the FWER
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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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