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The distance between two random vectors with given dispersion matrices

1982; Elsevier BV; Volume: 48; Linguagem: Inglês

10.1016/0024-3795(82)90112-4

1873-1856

Ingram Olkin, Friedrich Pukelsheim,

Advanced Algebra and Geometry

For two p-dimensional random vectors X and Y with dispersion matrices Σ11 and Σ22, respectively, we determine that covariance matrix Ψ0 of X and Y that minimizes the L2-distance between X and Y. There is a dual to this problem that is of interest in another context.