Uniformity of Double Saddlepoint Conditional Probability Approximations

This paper presents results showing that the error involved in using the double saddlepoint distribution function approximations of Skovgaard (1987,J. Appl. Probab.24875–887) are uniformly bounded. Particular attention is paid to distributions of sufficient statistics arising from generalized linear models. This work is intended in part to validate the use of the Markov Chain Monte Carlo by Kolassa and Tanner (1994,J. Amer. Statist. Assoc.89697–702) using these conditional distribution function approximations.