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Biometrika 1983 70(2):411-420; doi:10.1093/biomet/70.2.411
© 1983 by Biometrika Trust
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Robustness and efficiency properties of scatter matrices

DAVID E. TYLER

Department of Mathematical Sciences, Old Dominion University Norfolk, Virginia, U.S.A.

The robustness and efficiency properties of likelihood ratio tests for functions of the population covariance matrix are studied. An alternative class of tests based upon affine-invariant M-estimates of scatter is proposed whenever the function of the covariance matrix is invariant under a common scale change. For such inferences, it is shown that a single scalar-valued index of efficiency is sufficient.

Key Words: Affine-invariant M-estimate • Asymptotic distribution • Covariance matrix • Elliptical distribution • Likelihood ratio test • Maximum likelihood test • Multivariate t


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