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On the distribution of Hotelling's one-sample T2 under moderate non-normality

Published online by Cambridge University Press:  14 July 2016

A. W. Davis
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Abstract

The asymptotic distribution of Hotelling's one-sample T2 in multivariate Edgeworth populations is expanded to terms of the first order. Comparison with published simulation results indicates that the result is quite useful, even in cases where the underlying population is not well represented by an Edgeworth expansion.

Keywords

MULTIVARIATE DISTRIBUTION THEORYHOTELLING'S GENERALIZED T2MARDIA'S MEASURES OF NON-NORMALITYMULTIVARIATE EDGEWORTH EXPANSIONDOUBLY NON-CENTRAL DISTRIBUTION
Type
Part 5 — Statistical Theory
Information
Journal of Applied Probability , Volume 19 , Issue A , 1982 , pp. 207 - 216
Copyright
Copyright © 1982 Applied Probability Trust 

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References

Arnold, H. J. (1964) Permutation support for multivariate techniques. Biometrika 51, 65–70.Google Scholar
Bingham, C. (1974) An identity involving partitional generalized binomial coefficients. J. Multivariate Anal. 4, 210–223.Google Scholar
Chase, G. R. and Bulgren, W. G. (1971) A Monte Carlo investigation of the robustness of T2. J. Amer. Statist. Assoc. 66, 499–502.Google Scholar
Constantine, A. G. (1963) Some non-central distribution problems in multivariate analysis. Ann. Math. Statist. 34, 1270–1285.Google Scholar
Davis, A. W. (1976) Statistical distributions in univariate and multivariate Edgeworth populations. Biometrika 63, 661–670.CrossRefGoogle Scholar
Davis, A. W. (1979) Invariant polynomials with two matrix arguments extending the zonal polynomials: applications to multivariate distribution theory. Ann. Inst. Statist. Math. 31, 465–485.Google Scholar
Davis, A. W. (1980a) Invariant polynomials with two matrix arguments, extending the zonal polynomials. In Multivariate Analysis V, ed. Krishnaiah, P. R., 287–299. North-Holland, Amsterdam.Google Scholar
Davis, A. W. (1980b) On the effects of moderate multivariate nonnormality on Wilks's likelihood ratio criterion. Biometrika 67, 419–427.Google Scholar
Eaton, M. L. and Efron, B. (1970) Hotelling's T2 test under symmetry conditions. J. Amer. Statist. Assoc. 65, 702–711.Google Scholar
Everitt, B. S. (1979) A Monte Carlo investigation of the robustness of Hotelling's one- and two-sample T2 tests. J. Amer. Statist. Assoc. 74, 48–51.Google Scholar
Gayen, A. K. (1949) The distribution of ‘Student's’ t in random samples of any size drawn from non-normal universes. Biometrika 37, 236–255.Google Scholar
James, A. T. (1964) Distributions of matrix variates and latent roots derived from normal samples. Ann. Math. Statist. 35, 475–501.CrossRefGoogle Scholar
Kaplan, E. L. (1952) Tensor notation and the sampling cumulants of k -statistics. Biometrika 39, 319–323.Google Scholar
Mardia, K. V. (1970) Measures of multivariate skewness and kurtosis with applications. Biometrika 57, 519–530.Google Scholar
Mardia, K. V. (1975) Assessment of multinormality and the robustness of Hotelling's T2 test. Appl. Statist. 24, 163–171.Google Scholar
Marshall, A. W. and Olkin, I. (1967) A multivariate exponential distribution, J. Amer. Statist. Assoc. 62, 30–44.Google Scholar
Moran, P. A. P. (1975) What should a professor of statistics do? Austral. J. Statist. 17, 121–133.Google Scholar
Tiku, M. L. (1964) Approximating the general non-normal variance-ratio sampling distributions. Biometrika 51, 83–95.CrossRefGoogle Scholar