Saddlepoint method for obtaining tail probability of Wilks' likelihood ratio test

AbstractUsing the saddlepoint method, two explicit approximation formulae are given for the tail probability of Wilks' likelihood ratio criterion. A comparison with the exact probability shows that these approximations are very good even for small error degrees of freedom. A comparison with the asymptotic expansion obtained by Box (1949, Biometrika 36 317–346) is also given