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Generalized P ‐values and Bayesian evidence in the one‐sided testing problems under exponential distributions
Author(s) -
Yin Yuliang
Publication year - 2011
Publication title -
statistica neerlandica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.52
H-Index - 39
eISSN - 1467-9574
pISSN - 0039-0402
DOI - 10.1111/j.1467-9574.2011.00487.x
Subject(s) - frequentist inference , nuisance parameter , bayesian probability , mathematics , econometrics , exponential function , statistics , variety (cybernetics) , bayesian inference , estimator , mathematical analysis
The problem of comparing the frequentist evidence and the Bayesian evidence in the one‐sided testing problems has been widely treated and many researches revealed that these two methods can reach an agreement approximately. However, most of the previous work dealt mainly with situations without nuisance parameters. Since the presence of nuisance parameters is very common in practice, whether these two kinds of evidence still reach an agreement is a problem worthy of study. In this article, we establish in a systematic way under the exponential distributions the agreement of the Bayesian evidence and the generalized frequentist evidence (the generalized P ‐value) for a variety of one‐sided testing problems where the nuisance parameters are involved.