Abstract
We propose and examine statistical test-strategies that are somewhat between the maximum likelihood ratio and Bayes factor methods that are well addressed in the literature. The paper shows an optimality of the proposed tests of hypothesis. We demonstrate that our approach can be easily applied to practical studies, because execution of the tests does not require deriving of asymptotical analytical solutions regarding the type I error. However, when the proposed method is utilized, the classical significance level of tests can be controlled.
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References
Aitkin M (1991) Posterior Bayes factors. J R Stat Soc B 53: 111–142
Berger JO (1993) Statistical decision theory and bayesian analysis, 2nd edn. Springer Series in Statistics, New York
Brown RL, Durbin J, Evans JM (1975) Techniques for testing the constancy of regression relationships over time (with discussion). J R Stat Soc B 37: 149–192
Fisher RA (1925) Statistical methods for research workers, 1st edn. Oliver and Boyd, Edinburgh
Gelfand AE, Dey DK (1994) Bayesian model choice: asymptotics and exact calculations. J R Stat Soc B 56: 501–514
Green PJ (1990) On use of the EM for penalized likelihood estimation.. J R Stat Soc B 52: 443–452
Kass RE, Wasserman L (1995) A reference Bayesian test for nested hypotheses and its relationship to the Schwarz criterion. J Am Stat Assoc 90: 928–934
Krieger AM, Pollak M, Yakir B (2003) Surveillance of a simple linear regression. J Am Stat Assoc 98: 456–469
Lehmann EL, Romano JP (2005) Testing statistical hypotheses. Springer, New York
Marden JI (2000) Hypothesis testing: from p values to Bayes factors. J Am Stat Assoc 95: 1316–1320
Neyman J, Pearson E (1928) On the use and interpretation of certain test criteria for purposes of statistical inference: Part I. Biometrika 20A: 175–240
Neyman J, Pearson E (1928) On the use and interpretation of certain test criteria for purposes of statistical inference: Part II. Biometrika 20A: 263–294
Neyman J, Pearson E (1933) On the testing of statistical hypotheses in relation to probability a priori. Proc Camb Philos Soc 29: 492–510
Neyman J, Pearson E (1933) On the problem of the most efficient tests of statistical hypotheses. Philos Trans R Soc A 231: 289–337
Neyman J, Pearson E (1936) Contributions to the theory of testing statistical hypotheses. I. Unbiased critical region of type A and type A. Stat Res Mem 1: 1–37
Neyman J, Pearson E (1936) Sufficient statistics and uniformly most powerful tests of statistical hypotheses. Stat Res Mem 1: 113–137
Neyman J, Pearson E (1938) Contributions to the theory of testing statistical hypotheses. II. Stat Res Mem 2: 25–57
O’Hagan A (1995) Fractional Bayes factors for model comparison. J R Stat Soc B 57: 99–138
Pearson K (1900) On the criterion that a given system of deviation from the probable in the case of a correlated system of variables is such that it can be reasonably supposed to have arisen from random sampling. Philos Mag Ser 5 50: 157–172
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Vexler, A., Wu, C. & Yu, K.F. Optimal hypothesis testing: from semi to fully Bayes factors. Metrika 71, 125–138 (2010). https://doi.org/10.1007/s00184-008-0205-4
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DOI: https://doi.org/10.1007/s00184-008-0205-4