Abstract
The multivariate maximum squared-radii (MMSR) statistic is commonly used to detect multivariate outliers. We characterize the general form of the nonnegative-definite observation covariance structure for which the distribution of the MMSR statistic is the sameas the distribution resulting from the usual independence covariance structure. Thus, we extend the work of Young, Seaman, and Meaux (1992), who have characterized the general form of the positive-definite independence-distribution-preserving (IDP) dependency structure for the MMSR statistic. We also improve upon the results of Younget al (1992) in that we give a more complete and simple proof of the characterization of the general positive-definite IDP covariance structure for the MMSR statistic.
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References
Baksalary, J.K. (1984). Nonnegative definite and positive definite solutions to the matrix equationAXA *=B.Linear and Multilinear Algebra 16, 133–139.
Baksalary, J.K. and Puntanen, S. (1990). A complete solution to the problem of robustness of Grubbs’ test.Canad. Statist. 18, 285–287.
Fattorini, L. (1982). Assessing multivariate normality on beta plots.Statistica 42, 251–257.
Halperin, M. (1951). Normal regression theory in the presence of intra-class correlation.Ann. Math. Statist. 22, 573–580.
Hawkins, D.M. (1981). A new test for multivariate normality and homoscedasticity.Technometrics 23, 105–110.
Marco, V.R., Young, D.M., and Turner, D.W. (1987). A note on the effect of simple equicorrelation in detecting a spurious multivariate observation.Comm. Statist. Theor. and Meth. 16, 1027–1036.
Paulson, A. S., Roohan, P., and Sullo, P. (1987). Some empirical distribution function tests for multivariate normality.J. Statist. Comput. Simul. 28, 15–30.
Pavur, R.J. and Young, D.M. (1991). Conditions for the invariance for the multivariate versions of Grubbs’ test and Bartlett’s test under a general dependency structure.Metrika 38, 83–97.
Srivastava, M.S. (1980). Effect of equicorrelation in detecting a spurious observation.Canad. J. Statist. 2, 249–254.
Walsh, E. J. (1947). Concerning the effect of intraclass correlation on certain significance tests.Ann. Math. Statist. 18, 88–96.
Young, D.M., Pavur, R.J., and Marco, V.R. (1989). On the effect of correlation and unequal variances in detecting a spurious observation.Canadian J. Statist. 17, 103–105.
Young, D.M., Seaman, J.W., Jr., and Meaux, L.M. (1992). A characterization of the independence-distribution preserving covariance structure for the multivariate maximum squared-radii statistic.Comm. in Statist.: Theory and Methods 21, 1605–1613.
Young, D.M., Seaman, J.W., Jr., and Meaux, L.M. (1994). Independence distribution preserving dependency structures for the modified likelihood ratio test for detecting unequal covariance matrices.Statistics and Probability Letters 21, 395–403.
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Meaux, L.M., Young, D.M. & Seaman, J.W. A characterization of nonnegative-definite independence distribution-preserving covariance structures for the maximum squared-radii statistic. Statistical Papers 37, 375–382 (1996). https://doi.org/10.1007/BF02926115
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DOI: https://doi.org/10.1007/BF02926115