Printed in Great Britain Randomization distributions and saddlepoint approximations in generalized linear models

Various randomization distributions are shown to arise as conditional distributions in the setting of generalized linear models. These conditional distributions admit saddlepoint approximations which can obviate the need to simulate the randomization distributions they approximate. Examples include multinomial and Dirichlet bootstraps, the jackknife, and permutation distributions. The double saddlepoint approximation in a regular exponential family is shown to be equivalent to conditional use of a single saddlepoint approximation when the exponential family admits to a cut