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Q64Section III (Statistics)64 of 84

MLR makes the MP test for one θ1>θ0\theta_1>\theta_0 UMP for all of them

Let X1,…,XnX_1,\dots,X_n be a random sample from one-parameter exponential family of distributions, which has monotone likelihood ratio in statistic T(x‾)T(\underline x). Suppose H0:θ=θ0H_0:\theta=\theta_0 against H1:θ=θ1H_1:\theta=\theta_1 (θ1>θ0\theta_1>\theta_0) is to be tested. Then MP test based on T(x‾)T(\underline x) for testing H0H_0 against H1H_1 is:

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