Bayesian properties of the signed root likelihood ratio statistic are analysed. Conditions for first-order probability matching are derived by the examination of the Bayesian posterior and frequentist means of this statistic. Second-order matching conditions are shown to arise from matching of...

Objective Bayes methodology is considered for conditional frequentist inference about a canonical parameter in a multi-parameter exponential family. A condition is derived under which posterior Bayes quantiles match the conditional frequentist coverage to a higher-order approximation in terms of...

This paper concerns high-order inference for scalar parameters that are estimated by functions of multivariate M-estimators. Asymptotic formulae for the bias and skewness of the studentised statistic are derived. Although these formulae appear complicated, they can be evaluated easily by using...