MOMENTS FOR LEFT ELLIPTICALLY CONTOURED RANDOM MATRICES

[摘要] For a left elliptically contoured n x p random matrix Y approximately LEC(nxp)(mu, K, phi), the mth order moment E(x(m) Y) is obtained in terms of mu, K, and phi. When K = B x C, LEC(nxp)(mu, K, phi) is the conventional multivariate left elliptically contoured distribution MLEC(mu, A x SIGMA, phi), where A = B'B and SIGMA = C'C. Even if Y approximately N(nxp)(mu, SIGMA(Y)), the formula given here is new in that mu need not be 0 and SIGMA(Y) need not have the form A x SIGMA. (C) 1994 Academic Press, Inc.

[发布日期] 1994-04-01

[关键词] CHARACTERISTIC FUNCTION;HIGHER ORDER MOMENTS;INNER PRODUCT;KRONECKER (TENSOR) PRODUCT;MULTILINEAR DIFFERENTIAL;MULTIVARIATE LEFT ELLIPTICALLY CONTOURED DISTRIBUTION;PERMUTATION AND REINDEXING;STIEFEL MANIFOLD;ZONAL POLYNOMIAL