General Saddlepoint Approximations: Application to the Anderson-Darling Test Statistic
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Bibliographic record
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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| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.003 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
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