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.

当考虑高阶渐近性，匹配先验和基于关键量的置信度分布时，我们讨论并刻画了常客，置信度分布和客观贝叶斯推断之间的联系。重点是在目标标量参数上测试精确或尖锐的零假设。此外，我们说明，与标准一阶理论的应用相比，这些程序的应用几乎不需要额外的工作。在这方面，使用R软件，我们将说明如何在实验室间研究的数据，应力-强度可靠性以及剂量-响应数据的增长曲线的背景下，通过三个示例在实践中进行计算。