General Saddlepoint Approximations: Application to the Anderson-Darling Test Statistic
We consider the relative merits of various saddlepoint approximations for the c.d.f. of a statistic with a possibly non-normal limit distribution. In addition to the usual Lugannani-Rice approximation we also consider approximations based on higher-order expansions, including the case where the base distribution for the approximation is taken to be non-normal. This extends earlier work by Wood et al. (1993). These approximations are applied to the distribution of the Anderson-Darling test statistic. While these generalizations perform well in the middle of the distribution’s support, a conventional normal-based Lugannani-Rice approximation (Giles, 2001) is superior for conventional critical regions.
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- David E. A. Giles, 2000. "A Saddlepoint Approximation to the Distribution Function of the Anderson-Darling Test Statistic," Econometrics Working Papers 0005, Department of Economics, University of Victoria.
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