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General Saddlepoint Approximations: Application to the Anderson-Darling Test Statistic

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Abstract

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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  • Qian Chen & David E. Giles, 2007. "General Saddlepoint Approximations: Application to the Anderson-Darling Test Statistic," Econometrics Working Papers 0702, Department of Economics, University of Victoria.
    • Handle: RePEc:vic:vicewp:0702
    Note: ISSN 1485-6441
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    File URL: https://www.uvic.ca/socialsciences/economics/_assets/docs/econometrics/ewp0702.pdf
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    References listed on IDEAS

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    1. Ronchetti, Elvezio, 1990. "Small sample asymptotics: a review with applications to robust statistics," Computational Statistics & Data Analysis, Elsevier, vol. 10(3), pages 207-223, December.
    2. 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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    Keywords

    Saddlepoint approximation; goodness-of-fit; Anderson-Darling test;
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    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C46 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Specific Distributions

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