Objective Bayes, conditional inference and the signed root likelihood ratio statistic

TL;DR

This paper analyzes the Bayesian properties of the signed root likelihood ratio statistic, deriving conditions for probability matching and discussing implications for ancillary statistic models.

Contribution

It provides new conditions for first- and second-order probability matching of the signed root likelihood ratio statistic in Bayesian and frequentist frameworks.

Findings

Conditions for first-order probability matching are derived.

Second-order matching conditions relate to variance matching of a mean-adjusted statistic.

Conditional probability matching conditions are established for ancillary statistic models.

Abstract

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 the Bayesian posterior and frequentist variances of a mean-adjusted version of the signed root statistic. Conditions for conditional probability matching in ancillary statistic models are derived and discussed.