General Saddlepoint Approximations: Application to the Anderson-Darling Test Statistic |
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Authors: | Qian Chen |
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Institution: | School of Public Finance and Public Policy , Central University of Finance and Economics , Beijing, People's Republic of China |
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Abstract: | We consider the relative merits of various saddlepoint approximations for the cumulative distribution function (cdf) 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
Wood , A. T. A. ,
Booth , J. G. ,
Butler , R. W. ( 1993 ). Saddlepoint approximations to the CDF of some statistics with nonnormal limit distributions . Journal of the American Statistical Association 88 : 680 – 686 .Taylor & Francis Online], Web of Science ®] , Google Scholar]). 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
Giles , D. E. A. ( 2001 ). A Saddlepoint approximation to the distribution function of the Anderson-Darling test statistic . Communications in Statistics B 30 : 899 – 905 .Taylor & Francis Online] , Google Scholar]) is superior for conventional critical regions. |
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Keywords: | Anderson-Darling test Goodness-of-fit Saddlepoint approximation |
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