Search results for "Equivariant map"
showing 2 items of 22 documents
Influence functions and efficiencies of the canonical correlation and vector estimates based on scatter and shape matrices
2006
In this paper, the influence functions and limiting distributions of the canonical correlations and coefficients based on affine equivariant scatter matrices are developed for elliptically symmetric distributions. General formulas for limiting variances and covariances of the canonical correlations and canonical vectors based on scatter matrices are obtained. Also the use of the so-called shape matrices in canonical analysis is investigated. The scatter and shape matrices based on the affine equivariant Sign Covariance Matrix as well as the Tyler's shape matrix serve as examples. Their finite sample and limiting efficiencies are compared to those of the Minimum Covariance Determinant estima…
On the classification of CAT(0) structures for the 4-string braid group
2005
This paper is concerned with the class of so-called CAT(0) groups, namely, those groups that admit a geometric (i.e., properly discontinuous, co-compact, and isometric) action on some CAT(0) space. More precisely, we are interested in knowing to what extent it is feasible to classify the geometric CAT(0) actions of a given group (up to, say, equivariant homothety of the space). A notable example of such a classification is the flat torus theorem, which implies that the minimal geometric CAT(0) actions of the free abelian group Z (n ≥ 1) are precisely the free actions by translations of Euclidean space E. Typically, however, a given group will have uncountably many nonequivalent actions, mak…