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

Jorge Arevalillo ()

Metrika: International Journal for Theoretical and Applied Statistics, 2012, vol. 75, issue 8, 1009-1024

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

Keywords: Asymptotic statistics; Edgeworth expansion; r* saddlepoint approximation; Cumulants (search for similar items in EconPapers)
Date: 2012
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s00184-011-0365-5

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