Abstract
The Edgeworth approximation and the saddlepoint approximation are common procedures for approximating the distribution of a statistic based on n samples. The former is determined by the method of inverting the characteristic function which is expanded into powers of n-1/2, the latter is the approximate formula of the Fourier inversion integral. In this paper, we show that the third order Edgeworth approximation is obtained by expanding the saddlepoint approximation. This is performed through the perturbated solution for the saddlepoint which gives the latter approximation. Furthermore, a numerical example for an estimator of the Gaussian AR(1) process is provided.
