Improved prediction limits for continuous and discrete observations in generalised linear models

Abstract

Recent papers by Barndorff‐Nielsen & Cox (1996) and Vidoni (1998) concern the determination of prediction limits for an unobserved continuous random variable, for which the coverage probability equals the target value to third‐order accuracy. These results are usually expressed by means of the predictive density which generates the required prediction limit as the corresponding quantile. This paper discusses first the case where the variable to be predicted is discrete. This case requires special consideration, since a direct application of the above mentioned results is not possible. Secondly, these prediction limits, and the corresponding predictive distributions, are computed for both discrete and continuous generalised linear models.