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A law of the iterated logarithm for weakly exchangeable arrays

Published online by Cambridge University Press:  24 October 2008

D. J. Scott  and
R. M. Huggins
D. J. Scott
Affiliation:
Department of Statistics, La Trobe University, Bundoora, Victoria 3083, Australia
R. M. Huggins
Affiliation:
Department of Statistics, La Trobe University, Bundoora, Victoria 3083, Australia
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Extract

In Eagleson and Weber [2] a central limit theorem for weakly exchangeable arrays is given as a consequence of a reverse martingale central limit theorem. As noted in their remarks, a direct application of this is a central limit theorem for the classical U-statistics. Here we give a corollary to the functional law of the iterated logarithm of Scott and Huggins [4] and use this to obtain laws of the iterated logarithm for weakly exchangeable arrays and hence for U-statistics under a finite (2 + δ)th moment condition.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 98 , Issue 3 , November 1985 , pp. 541 - 545
Copyright
Copyright © Cambridge Philosophical Society 1985

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References

REFERENCES

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