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Biometrika 1982 69(2):429-436; doi:10.1093/biomet/69.2.429
© 1982 by Biometrika Trust
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Radial estimates and the test for sphericity

DAVID E. TYLER

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

The first two moments for random symmetric matrices with radial distributions are given. This result enables one to generalize asymptotic procedures based on the sample covariance matrix to procedures based on a class of estimates for a positive-definite matrix parameter. This class includes the maximum likelihood estimates for the scatter matrix of an elliptical population, and affine-invariant robust estimates of a scatter matrix. Application of the results to the test for sphericity is illustrated.

Key Words: Affine-invariant robust estimate • Asymptotic distribution • Elliptical distribution • Maximum likelihood estimate • Radial distribution and estimate • Rotatable distribution • Sphericity test


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