Improving on the Best Affine Equivariant Estimator of the Ratio of Generalized Variances

Author： Iliopoulos G.   Kourouklis S.  

Publisher： Academic Press

ISSN： 0047-259X

Source： Journal of Multivariate Analysis, Vol.68, Iss.2, 1999-02, pp. : 176-192

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Abstract

We consider the problem of decision-theoretic estimation of the ratio of generalized variances of two matrix normal distributions with unknown means under a general loss function. The inadmissibility of the best affine equivariant estimator is established by exhibiting various improved estimators. In particular, under certain conditions on the loss, two classes of improved procedures based on all the available data are presented. As a preliminary result of independent interest, an improved estimator of an arbitrary power of the generalized variance of a matrix normal distribution with an unknown mean is derived under a general strictly bowl-shaped loss. Copyright 1999 Academic Press.

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