Sankhya: The Indian Journal of Statistics
2002, Volume 64, Series B, Pt. 1, 11--25
INFERENCES USING A STRUCTURED FOURTH-ORDER MOMENT MATRIX
JAMES R. SCHOTT, University of Central Florida, Orlando, USA
SUMMARY. In this paper, we consider a parameterization for the fourth-order moment matrix of a random vector. This parameterization includes that of an elliptical distribution as a special case and can be used in the construction of robust tests for covariance matrices. Consistent estimates of the parameters in this fourth-order moment matrix are obtained. As an example of the use of the estimated fourth-order moment matrix, we obtain a statistic for testing the hypothesis that the covariance matrix is equal to some prespecified matrix.
AMS (1991) subject classification. 62H15, 62H12.
Key words and phrases. Covariance matrices; elliptical distribution; robust tests.
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