Acta Mathematicae Applicatae Sinica

, Volume 13, Issue 1, pp 64–70 | Cite as

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

  • Li Runze 
Article

Abstract

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 ofC φ κ,λ (BR,BU),Cκ(BR)Cλ(BU) andCκ(B−1U), whereBB d =X′X andXn×p is distributed according to an elliptical matrix distribution. We also give their applications in multivariate distribution theory including the related development in econometrics.

Key words

Elliptical matrix distributions invariant polynomials zonal polynomials 

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Copyright information

© Science Press, Beijing, China and Allerton Press, Inc., New York, U.S.A. 1997

Authors and Affiliations

  • Li Runze 
    • 1
  1. 1.Probability LaboratoryInstitute of Applied Mathematics, the Chinese Academy of SciencesBeijingChina

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