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Laplace approximations to hypergeometric functions of two matrix arguments

Author

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  • Butler, Ronald W.
  • Wood, Andrew T.A.

Abstract

We present a unified approach to Laplace approximation of hypergeometric functions with two matrix arguments. The general form of the approximation is designed to exploit the Laplace approximations to hypergeometric functions of a single matrix argument presented in Butler and Wood (Ann. Statist. 30 (2002) 1155, Laplace approximations to Bessel functions of matrix argument, J. Comput. Appl. Math. 155 (2003) 359) which have proved to be very accurate in a variety of settings. All but one of the approximations presented here appear to be new. Numerical accuracy is investigated in a number of statistical applications.

Suggested Citation

  • Butler, Ronald W. & Wood, Andrew T.A., 2005. "Laplace approximations to hypergeometric functions of two matrix arguments," Journal of Multivariate Analysis, Elsevier, vol. 94(1), pages 1-18, May.
    • Handle: RePEc:eee:jmvana:v:94:y:2005:i:1:p:1-18
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    References listed on IDEAS

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    1. Glynn, William J. & Muirhead, Robb J., 1978. "Inference in canonical correlation analysis," Journal of Multivariate Analysis, Elsevier, vol. 8(3), pages 468-478, September.
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    Cited by:

    1. Daya K. Nagar & Raúl Alejandro Morán-Vásquez & Arjun K. Gupta, 2015. "Extended Matrix Variate Hypergeometric Functions and Matrix Variate Distributions," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2015, pages 1-15, January.
    2. I. M. Johnstone & B. Nadler, 2017. "Roy’s largest root test under rank-one alternatives," Biometrika, Biometrika Trust, vol. 104(1), pages 181-193.
    3. Koki Shimizu & Hiroki Hashiguchi, 2024. "Chi-Square Approximation for the Distribution of Individual Eigenvalues of a Singular Wishart Matrix," Mathematics, MDPI, vol. 12(6), pages 1-11, March.

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