H-likelihood Predictive Intervals for Unobservables

Inferences about unobserved random variables, such as future observations, random effects and latent variables, are of interest. In this paper, to make probability statements about unobserved random variables without assuming priors on fixed parameters, we propose the use of the confidence distribution for fixed parameters. We focus on their interval estimators and related probability statements. In random-effect models, intervals can be formed either for future (yet-to-be-realised) random effects or for realised values of random effects. The consistency of intervals for these two cases requires different regularity conditions. Via numerical studies, their finite sampling properties are investigated.