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Biometrika 1990 77(4):787-796; doi:10.1093/biomet/77.4.787
© 1990 by Biometrika Trust
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Randomization distributions and saddlepoint approximations in generalized linear models

JAMES G. BOOTH and RONALD W. BUTLER

Department of Statistics, University of Florida Gainesville, Florida 32611, U.S.A.
Department of Statistics, Colorado State University Fort Collins, Colorado 80523, U.S.A.

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.

Key Words: Bootstrap • Cut • Estimating equation • Generalized linear model • Jackknife • Permutation distribution • Saddlepoint approximation


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E. F. Abd-Elfattah and R. W. Butler
The weighted log-rank class of permutation tests: P-values and confidence intervals using saddlepoint methods
Biometrika, August 5, 2007; (2007) asm060v1.
[Abstract] [PDF]


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