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Asymptotic Statistics by A.W. van der Vaart

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14

Relative Efficiency of Tests

           The quality of sequences of tests can be judged from their power at alternatives that become closer and closer to the null hypothesis. This motivates the study of local asymptotic power functions. The relative efficiency of two sequences of tests is the quotient of the numbers of observations needed with the two tests to obtain the same level and power. We discuss several types of asymptotic relative efficiencies.

14.1 Asymptotic Power Functions

Consider the problem of testing a null hypothesis H0 : θ ∈ Θ0 versus the alternative H1 : θ ∈ Θ1. The power function of a test that rejects the null hypothesis if a test statistic falls into a critical region Kn is the function , which gives the probability of ...

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