On the cumulants of affine equivariant estimators in elliptical families

Rudolf Grübel and David M. Rocke

Journal of Multivariate Analysis, 1990, vol. 35, issue 2, 203-222

Abstract: Given a statistical model for data which take values in Rd and have elliptically distributed errors, and affine equivariant estimators [mu] and [mu] of a mean vector in Rd[circle times operator]Rn and a d - d scatter matrix, expressions are given for the covarances of the estimators in terms of their expectations and some unknown constants that depend on the model and the estimator. Higher order cumulants are also developed. These results place considerable constraints on the possible cumulants of [mu] and [mu], as wel as those of estimators of higher order behavior such as multivariate skewness and kurtosis. These expressions are obtained using tensor methods.

Keywords: maximum; likelihood; multivariate; location; multivariate; regression; robust; estimation; seemingly; unrelated; regression; tensor; methods (search for similar items in EconPapers)
Date: 1990
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