TY - JOUR

T1 - The expected values of invariant polynomials with matrix argument of elliptical distributions

AU - Li, Runze

N1 - Funding Information:
Received July 30, 1993. Revised February 21, 1995. * This research is supported by the Chinese Academy of Sciences.

PY - 1997

Y1 - 1997

N2 - Invariant polynomials with matrix arguments have been defined by the theory of group representation, generalizing the zonal polynomials. They have developed as a useful tool to evaluate certain integrals arising in multivariate distribution theory, which were expanded as power series in terms of the invariant polynomials. Some interesting polynomials has been shown by people working in the field of econometric theory. In this paper, we derive the expected values of Cφκ,λ(BR,BU), C κ(BR)Cλ(BU) and Cκ(B -1U), where B=dX′X and Xnxp is distributed according to an elliptical matrix distribution. We also give their applications in multivariate distribution theory including the related development in econometrics.

AB - Invariant polynomials with matrix arguments have been defined by the theory of group representation, generalizing the zonal polynomials. They have developed as a useful tool to evaluate certain integrals arising in multivariate distribution theory, which were expanded as power series in terms of the invariant polynomials. Some interesting polynomials has been shown by people working in the field of econometric theory. In this paper, we derive the expected values of Cφκ,λ(BR,BU), C κ(BR)Cλ(BU) and Cκ(B -1U), where B=dX′X and Xnxp is distributed according to an elliptical matrix distribution. We also give their applications in multivariate distribution theory including the related development in econometrics.

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U2 - 10.1007/BF02020482

DO - 10.1007/BF02020482

M3 - Article

AN - SCOPUS:53249133078

VL - 13

SP - 64

EP - 70

JO - Acta Mathematicae Applicatae Sinica

JF - Acta Mathematicae Applicatae Sinica

SN - 0168-9673

IS - 1

ER -