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Edgeworth expansion of the distribution of Stein's statistic

Published online by Cambridge University Press:  24 October 2008

Peter Hall
Peter Hall
Affiliation:
Australian National University
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Abstract

We derive a two-term Edgeworth expansion for the distribution of Stein's double sampling statistic in the case of a non-normal parent population. The first term describes the main effect of skewness, while the second describes the main effect of kurtosis and the secondary effect of skewness. The remainder is shown to be uniformly negligible in comparison with these effects. Explicit conditions are given for the expansion to be valid. These conditions are considerably weaker than those which were imposed in an earlier derivation of the ‘exact’ distribution of Stein's statistic.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 93 , Issue 1 , January 1983 , pp. 163 - 175
Copyright
Copyright © Cambridge Philosophical Society 1983

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References

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