The Annals of Statistics

Complete Class Results for Hypothesis Testing Problems with Simple Null Hypotheses

Lawrence D. Brown and John I. Marden

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Hypothesis testing problems in which the null hypothesis is simple, the parameter space is finite dimensional and the supports of the probability measures are independent of the parameter are considered. Essentially complete class results are obtained for characterizing the limits of Bayes tests. Conditions for tests to be admissible and the class to be complete are given. Results are then specialized to exponential families, along with some illustrative examples.

Article information

Ann. Statist., Volume 17, Number 1 (1989), 209-235.

First available in Project Euclid: 12 April 2007

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Primary: 62C07: Complete class results
Secondary: 62F05: Asymptotic properties of tests 62H15: Hypothesis testing 62C10: Bayesian problems; characterization of Bayes procedures 62H20: Measures of association (correlation, canonical correlation, etc.) 62J10: Analysis of variance and covariance

Complete class admissibility hypothesis tests Bayes tests exponential families invariant tests


Brown, Lawrence D.; Marden, John I. Complete Class Results for Hypothesis Testing Problems with Simple Null Hypotheses. Ann. Statist. 17 (1989), no. 1, 209--235. doi:10.1214/aos/1176347012.

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