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Biometrika 1994 81(2):271-278; doi:10.1093/biomet/81.2.271
© 1994 by Biometrika Trust
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Multiparameter testing in exponential models: Third order approximations from likelihood

P. K. CHEAH1, D. A. S. FRASER2 and N. REID3

1Department of Statistics, University of Toronto Toronto, Canada, M5S1A1
2Department of Mathematics and Statistics, York University North York, Canada, M3J 1P3
3Department of Statistics, University of Toronto Toronto, Canada, M5S 1A1

For composite testing of several canonical components in an exponential model, a conical or directional test provides a one-dimensional measure of departure. We approximate the distribution of this test statistic to third order by numerical inversion of a profile likelihood. The method extends the Lugannani & Rice type formula to kernels other than the normal.

Key Words: Approximate distribution • Asymptotic expansion • Conditional inference • Conditional likelihood • Exponential family • Lugannani & • Rice approximation • Saddlepoint approximation • Tail probability


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