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A Saddlepoint Approximation to the Distribution Function of the Anderson-Darling Test Statistic

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  • David E. A. Giles

Abstract

The Anderson-Darling goodness-of-fit test has a highly skewed and non-standard limit distribution. Various attempts have been made to tabulate the associated critical points, using both theoretical approximations and simulation methods. We show that a standard saddlepoint approximation performs well in both tails of the distribution. It is markedly superior to other theoretical approximations in the lower tail of the distribution.

Suggested Citation

  • 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.
    • Handle: RePEc:vic:vicewp:0005
    Note: ISSN 1485-6441
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    File URL: https://www.uvic.ca/socialsciences/economics/_assets/docs/econometrics/ewp0005.pdf
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    Citations

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    Cited by:

    1. 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.
    2. Qian Chen & David E. Giles, 2007. "A Saddlepoint Approximation to the Distribution of the Half-Life Estimator in an Autoregressive Model: New Insights Into the PPP Puzzle," Econometrics Working Papers 0703, Department of Economics, University of Victoria.
    3. Christopher Withers & Saralees Nadarajah, 2010. "Tilted Edgeworth expansions for asymptotically normal vectors," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 62(6), pages 1113-1142, December.

    More about this item

    Keywords

    preliminary testing; risk function; Bayes estimation;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General

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