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A tabular method for correcting skewness

Published online by Cambridge University Press:  24 October 2008

Peter Hall
Peter Hall
Affiliation:
Australian National University
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Abstract

We propose a smooth correction for skewness in an asymptotically normal statistic. Unlike the case of approximation by Edgeworth expansion, our correction applies uniformly in all values of the level. The correction is based on a ' comparison statistic', and, in the case of the Studentized mean, it enables removal of all effects of skewness up to terms of order .

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 97 , Issue 3 , May 1985 , pp. 525 - 540
Copyright
Copyright © Cambridge Philosophical Society 1985

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References

REFERENCES

[1]Barndorff-Nielsen, O. and Cox, D. R.. Edgeworth and saddle-point approximations with statistical applications (with Discussion). J. Royal Statist. Soc. 41 (1979), 279–312.Google Scholar
[2]Bhattacharya, R. N. and Ghosh, J. K.. On the validity of the formal Edgeworth expansion. Ann. Statist. 6 (1978), 434–451. Corrigendum Ann. Statist. 8, 1399.CrossRefGoogle Scholar
[3]Bhattacharya, R. N. and Ranga Rao, R.. Normal Approximation and Asymptotic Expansions (Wiley, 1976).Google Scholar
[4]Bowman, H., Beauchamp, J. and Shenton, L.. The distribution of the t-statistici under non-normality. Internat. Statist. Rev. 45 (1977), 233–242.CrossRefGoogle Scholar
[5]Chambers, J. M.. On methods of asymptotic approximation for multivariate distributions. Biometrika 54 (1967), 367–383.CrossRefGoogle ScholarPubMed
[6]Chibishov, D. M.. An asymptotic expansion for the distribution of a statistic admitting an asymptotic expansion Theor. Probability Appl. 17 (1972), 620–630.CrossRefGoogle Scholar
[7]Chibishov, D. M.. An asymptotic expansion for a class of estimates containing maximum likelihood estimates. Theor. Probability Appl. 18 (1973), 295–303.CrossRefGoogle Scholar
[8]Cressie, N.. Relaxing assumptions in the one-sample t-test. Aust. J. Statist. 22 (1980), 143–153.CrossRefGoogle Scholar
[9]Hall, P.. Inverting an Edgeworth expansion. Ann. Statist. 11 (1983), 569–576.Google Scholar
[10]Hall, P.. Chi square approximations to the distribution of a sum of independent random variables. Ann. Probability 11 (1983), 1028–1036.CrossRefGoogle Scholar
[11]Indritz, J.. Methods of Analysis (Macmillan, 1963).Google Scholar
[12]Pedersen, B. V.. Approximating conditional distributions by the mixed Edgeworth-saddlepoint expansion. Biometrika 66 (1979), 597–604.CrossRefGoogle Scholar
[13]Pfanzagl, J.. Asymptotic expansions in parametric statistical theory. In Developments in Statistics, vol. 3, ed. Krishnaiah, P. R., pp. 1–97. (Academic Press, 1980).Google Scholar