Some remarks on conditional and unconditional inference for location-scale models

Conditional and unconditional confidence intervals have been compared by Grice, Bain, and Engelhardt (Commun. Statist. B7 (1978), 515–524) in terms of the location-scale model with double-exponential distribution form. Preference was found for the conditional intervals based on mean length and coverage probability for untrue parameters values. These two criteria for a location-scale system are shown to be inappropriate criteria for assessing the conditional versus unconditional approaches to inference. The usual ancillarity concept is also noted to be inappropriate. Support for many conditional analyses, however, is found in a more careful formulation of the statistical model.