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A Survey on the Invariant Polynomials with Matrix Arguments in Relation to Econometric Distribution Theory

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  • Chikuse, Yasuko
  • Davis, A. W.

Abstract

Invariant polynomials with matrix arguments have been defined by the theory of group representations, 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 interest in the polynomials has been shown by people working in the field of econometric theory. In this paper, we shall survey the properties of the invariant polynomials and their applications in multivariate distribution theory including related developments in econometrics.

Suggested Citation

  • Chikuse, Yasuko & Davis, A. W., 1986. "A Survey on the Invariant Polynomials with Matrix Arguments in Relation to Econometric Distribution Theory," Econometric Theory, Cambridge University Press, vol. 2(2), pages 232-248, August.
    • Handle: RePEc:cup:etheor:v:2:y:1986:i:02:p:232-248_01
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    Cited by:

    1. Forchini, G., 2000. "The density of the sufficient statistics for a Gaussian AR(1) model in terms of generalized functions," Statistics & Probability Letters, Elsevier, vol. 50(3), pages 237-243, November.
    2. Dharmawansa, Prathapasinghe & McKay, Matthew R., 2011. "Extreme eigenvalue distributions of some complex correlated non-central Wishart and gamma-Wishart random matrices," Journal of Multivariate Analysis, Elsevier, vol. 102(4), pages 847-868, April.

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