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Asymptotic Statistics by A.W. van der Vaart

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15

Efficiency of Tests

           It is shown that, given converging experiments, every limiting power function is the power function of a test in the limit experiment Thus, uniformly most powerful tests in the limit experiment give absolute upper bounds for the power of a sequence of tests. In normal experiments such uniformly most powerful tests exist for linear hypotheses of codimension one. The one-sample location problem and the two-sample problem are discussed in detail, and appropriately designed (signed) rank tests are shown to be asymptotically optimal.

15.1 Asymptotic Representation Theorem

A randomized test (or test function) image in an ...

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