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On Hodges-Lehmann optimality of LR tests. (English) Zbl 0812.62019
Summary: It is shown that the likelihood ratio test statistics are Hodges-Lehmann optimal [J. L. Hodges and E. L. Lehmann, Ann. Math. Stat. 27, 324-335 (1956; Zbl 0075.292)] for testing the null hypothesis against the whole parameter space, provided that certain regularity conditions are fulfilled. These conditions are verified for the non-singular normal, multinomial and Poisson distribution.

62F03 Parametric hypothesis testing
62F05 Asymptotic properties of parametric tests
62G10 Nonparametric hypothesis testing
62H15 Hypothesis testing in multivariate analysis
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