Abstract
The modified Bayesian-Frequentist test of Berger, Brown and Wolpert (1994) is considered here in the context of normal hypothesis testing. We focus attention on the testing of a precise null hypothesis versus a composite alternative, either the one-sided or the two-sided type. We study the properties of the corresponding modified Bayesian-Frequentist test and in particular the large-sample behavior of its no decision region under two different classes of prior distributions, viz., the shifted conjugate class and a domain-restricted noninformative class. It is shown that under these prior classes, the size of the no-decision region of the test is rather small, compared to the relevant sample size. A lower bound on the conditional probability of the type I error is also provided.
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© 1997 Birkhäuser Boston
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Berger, J.O., Boukai, B., Wang, Y. (1997). Properties of Unified Bayesian-Frequentist Tests. In: Panchapakesan, S., Balakrishnan, N. (eds) Advances in Statistical Decision Theory and Applications. Statistics for Industry and Technology. Birkhäuser Boston. https://doi.org/10.1007/978-1-4612-2308-5_14
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DOI: https://doi.org/10.1007/978-1-4612-2308-5_14
Publisher Name: Birkhäuser Boston
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