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.
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Acknowledgements
This research work was partially supported by University of Padova (BIRD197903) and by PRIN 2015 (Grant 2015EASZFS_003). The authors wish to thank Nancy Reid for constructive comments on a draft version of the present paper. We are also grateful to the Editor and the referees for their valuable suggestions.
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Ruli, E., Ventura, L. Can Bayesian, confidence distribution and frequentist inference agree?. Stat Methods Appl 30, 359–373 (2021). https://doi.org/10.1007/s10260-020-00520-y
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DOI: https://doi.org/10.1007/s10260-020-00520-y