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Abstract:
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There has been resurgent research interest in confidence distribution (CD), which, though entirely a frequentist concept, has shown potential to provide a useful framework for connecting different statistical paradigms. Using CD, we develop a new framework for hypothesis testing. Unlike the typical three-step Neyman-Pearson testing procedure (i.e., construct a test statistic, establish its sampling distribution under the null hypothesis, obtain a p-value or a rejection region), the CD approach can derive a p-value directly, bypassing the first two steps. This derivation of p-values is similar in spirit to that of a posterior distribution in the Bayesian approach, but it requires no knowledge of priors. We also introduce "confidence-factor" ("C-factor" for short), which can be viewed as a frequentist analog to the Bayes-factor in Bayesian analysis. C-factor and Bayes-factor are shown to be identical when the underlying Bayesian posterior and CD coincide. These developments may provide direct connections and meaningful comparisons between testing results obtained from frequentist and Bayesian paradigms, and, hopefully, coherent inference outcomes for general scientific pursuits.
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