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The saddlepoint method is used to approximate to the distribution of an estimator defined by an estimating equation. Two different approaches are available, one of which is shown to be equivalent to the technique of Field & Hampel (1982). Two recent formulae for the tail probability, due to Lugannani & Rice (1980) and to Robinson (1982) respectively, which are uniformly accurate over the whole range of the estimator, are compared numerically with the exact results and those computed by Field & Hampel. They are found to be of comparable accuracy while avoiding the use of numerical integration. The most accurate is that of Lugannani & Rice.
Biometrika © 1983 Biometrika Trust