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Exploring the relation between the r* approximation and the Edgeworth expansion

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  • Jorge Arevalillo

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    Abstract

    In this paper we study the relation between the r* saddlepoint approximation and the Edgeworth expansion when quite general assumptions for the statistic under consideration are fulfilled. We will show that the two term Edgeworth expansion approximates the r* formula up to an O(n −3/2 ) remainder; this provides a new way of looking at the order of the error of the r* approximation. This finding will be used to inspect the close connection between the r* formula and the Edgeworth B adjustment introduced in Phillips (Biometrika 65:91–98, 1978 ). We will show that, whenever an Edgeworth expansion exists, this adjustment approximates both the distribution function of the statistic and the r* formula to the same order degree as the Edgeworth expansion. Some numerical examples for the sample mean and U-statistics are given in order to shed light on the theoretical discussion. Copyright Springer-Verlag 2012

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    File URL: http://hdl.handle.net/10.1007/s00184-011-0365-5
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    Bibliographic Info

    Article provided by Springer in its journal Metrika.

    Volume (Year): 75 (2012)
    Issue (Month): 8 (November)
    Pages: 1009-1024

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    Handle: RePEc:spr:metrik:v:75:y:2012:i:8:p:1009-1024

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    Web page: http://www.springerlink.com/link.asp?id=102509

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    Related research

    Keywords: Asymptotic statistics; Edgeworth expansion; r* saddlepoint approximation; Cumulants;

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    1. Monti, Anna Clara, 1993. "A new look at the relationship between Edgeworth expansion and saddlepoint approximation," Statistics & Probability Letters, Elsevier, vol. 17(1), pages 49-52, May.
    2. Killmann Frank & von Collani Elart, 2001. "A Note on the Convolution of the Uniform and Related Distributions and Their Use in Quality Control," Economic Quality Control, De Gruyter, vol. 16(1), pages 17-41, January.
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