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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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    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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    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
    DOI: 10.1007/s00184-011-0365-5
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    1. Killmann Frank & von Collani Elart, 2001. "A Note on the Convolution of the Uniform and Related Distributions and Their Use in Quality Control," Stochastics and Quality Control, De Gruyter, vol. 16(1), pages 17-41, January.
    2. 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.
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