Dispersion-diminishing transformations |
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| Authors: | D R Jensen D E Ramirez |
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| Institution: | 1. Department of Statistics , Virginia Polytechnic Institute , Blacksburg, VA, 24061;2. Department of Mathematics , University of Virginia , Charlottesville, VA, 22903 |
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| Abstract: | Let D(σ) consist of matrices congruent to and dominated by a given matrix σ , and let T(σ) be the corresponding congruent transformations. These classes are characterized and their properties studied when σ is positive definite. Dispersion orderings are considered, including dispersion-diminishing linear transformations, concentration properties of which are shown. Arbitrary linear transformations are decomposed into contractions, isometries and dilations on subspaces relative to Mahalanobis norms. Applications are noted in statistical process control and linear inference |
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| Keywords: | Matrix ordering congruence monotone functions dispersion reduction linear inference |
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