Can Bayesian, confidence distribution and frequentist inference agree?

Erlis Ruli () and Laura Ventura ()
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Erlis Ruli: University of Padova
Laura Ventura: University of Padova

Statistical Methods & Applications, 2021, vol. 30, issue 1, No 15, 359-373

Abstract: Abstract We discuss and characterise connections between frequentist, confidence distribution and objective Bayesian inference, when considering higher-order asymptotics, matching priors, and confidence distributions based on pivotal quantities. The focus is on testing precise or sharp null hypotheses on a scalar parameter of interest. Moreover, we illustrate that the application of these procedures requires little additional effort compared to the application of standard first-order theory. In this respect, using the R software, we indicate how to perform in practice the computation with three examples in the context of data from inter-laboratory studies, of the stress–strength reliability, and of a growth curve from dose–response data.

Keywords: Credible interval; First-order theory; Full Bayesian significance test; Higher-order asymptotics; Likelihood inference; Marginal posterior distribution; Matching prior; Pivotal quantity; Precise null hypothesis; p value; Tail area probability (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10260-020-00520-y

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