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Approximate Confidence Intervals for a Robust Scale Parameter

Published online by Cambridge University Press:  01 January 2025

David V. Budescu
David V. Budescu*
Affiliation:
University of North Carolina at Chapel Hill
*
Requests for reprints should be sent to David V. Budescu, L. L. Thurstone Psychometric Laboratory, Davie Hall 013-A, University of North Carolina, Chapel Hill, N.C. 27514.
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Abstract

A recent paper by Wainer and Thissen has renewed the interest in Gini’s mean difference, G, by pointing out its robust characteristics. This note presents distribution-free asymptotic confidence intervals for its population value, γ, in the one sample case and for the difference Δ = (γ1 − γ2) in the two sample situations. Both procedures are based on a technique of jackknifing U-statistics developed by Arvesen.

Keywords

robustnessGini’s mean differencejackknifingU-statistics
Type
Notes And Comments
Information
Psychometrika , Volume 45 , Issue 3 , September 1980 , pp. 397 - 402
Copyright
Copyright © 1980 The Psychometric Society

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Footnotes

The author would like to thank Dr. Mark I. Appelbaum for his useful comments on an earlier version of this manuscript.

References

Andrews, D. F., Bickel, P. J., Hampel, F. R., Huber, P. J., Rogers, W. H. & Tukey, J. W. Robust estimates of location, 1972, Princeton, N.J.: Princeton University.Google Scholar
Arvesen, J. N. Jackknifing U statistics. Annals of Mathematical Statistics, 1969, 40, 2076–2100.CrossRefGoogle Scholar
Arvesen, J. N. Correction of “Jackknifing U statistics. Annals of Mathematical Statistics, 1970, 41, 375–375.CrossRefGoogle Scholar
Arvesen, J. N., & Schmitz, T. H. Robust procedures for variance component problems using the jackknife. Biometrics, 1970, 26, 677–686.CrossRefGoogle Scholar
Arvesen, J. N., & Salsburg, D. S. Approximate tests and confidence intervals using the jackknife. In Elashoff, R. M. (Eds.), Perspectives in biometrics, 1975, New York: Academic Press.Google Scholar
Barnett, F. C., Mullen, K., & Shaw, J. G. Linear estimates of a population scale parameter. Biometrika, 1967, 54, 551–554.CrossRefGoogle ScholarPubMed
David, H. A. Gini’s mean difference rediscovered. Biometrika, 1968, 55, 573–575.Google Scholar
David, H. A. Order statistics, 1970, New York: Wiley.Google Scholar
Devlin, S. J., Gnanadesikan, R., & Kettenring, J. R. Robust estimation and outlier detection with correlation coefficients. Biometrika, 1975, 62, 531–546.CrossRefGoogle Scholar
Duncan, G. T., & Layard, M. W. J. A Monte Carlo study of asymptotically robust tests for correlation coefficients. Biometrika, 1973, 60, 551–558.CrossRefGoogle Scholar
Hampel, F. R. The influence curve and its role in robust estimation. Journal of the American Statistical Association, 1974, 69, 383–393.CrossRefGoogle Scholar
Hettmansperger, J. P., & McKean, J. W. Statistical inference based on ranks. Psychometrika, 1978, 43, 69–79.CrossRefGoogle Scholar
Hoeffding, W. A class of statistics with asymptotically normal distribution. Annals of Mathematical Statistics, 1948, 19, 293–325.CrossRefGoogle Scholar
Miller, R. G. The jackknife—a review. Biometrika, 1974, 61, 1–15.Google Scholar
Wainer, H. Robust statistics: A survey and some prescriptions. Journal of Educational Statistics, 1976, 1, 285–312.CrossRefGoogle Scholar
Wainer, H., & Thissen, D. Three steps towards robust regression. Psychometrika, 1976, 41, 9–34.CrossRefGoogle Scholar