Sankhya: The Indian Journal of Statistics

2002, Volume 64, Series B, Pt. 1, 11--25

INFERENCES USING A STRUCTURED FOURTH-ORDER MOMENT MATRIX

By

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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