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A predictive approach to some hypothesis testing problems. (English) Zbl 1254.62030

Summary: A new approach to testing statistical hypothesis is considered in this paper. The main departure from both classical and Bayesian testing is that the null and alternative hypothesis now refer to observable quantities, i.e. sample statistics, instead of model defining parameters. The idea for constructing the new tests for comparing two populations is based on the agreement between observed data or statistics and the corresponding predictive distributions, assuming that the resulting join sample, from the combination of the two samples, is exchangeable. This may result in that the null hypothesis may be neither rejected nor accepted, that is, the test may be inconclusive at some specified level or probabilistic content.
These ideas are illustrated and applied to some classical two-sample problems, where comparisons with the corresponding classical tests are considered, and extended to the testing of homogeneity of the sample medians of two populations and the classical Behrens-Fisher problem.

MSC:

62F15 Bayesian inference
62F03 Parametric hypothesis testing
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