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Biometrika 1992 79(1):157-169; doi:10.1093/biomet/79.1.157
© 1992 by Biometrika Trust
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Saddlepoint approximations for the generalized variance and Wilks' statistic

RONALD W. BUTLER1 and S. HUZURBAZAR1

1Department of Statistics, Colorado State University Fort Collins, CO 80523, U.S.A.
2Centre for Mathematics and its Applications, Australian National University GPO Box 4, Canberra, A.C.T. 2601, Australia

Probability distributions for the generalized variance and Wilks' likelihood ratio statistic in multivariate analysis are shown to arise as marginal and conditional distributions of canonical sufficient statistics in the setting of regression models with gamma errors and varying degrees of freedom. As such, appropriate saddlepoint methods are used to approximate tail probabilities.

Key Words: Gamma regression • Generalized variance • Saddlepoint approximation • Wilks' statistic


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