Distribution of the ratio of two Wishart matrices and cumulative probability evaluation by the holonomic gradient method

Hiroki Hashiguchi, Nobuki Takayama and Akimichi Takemura

Journal of Multivariate Analysis, 2018, vol. 165, issue C, 270-278

Abstract: We study the distribution of the ratio of two central Wishart matrices with different covariance matrices. We first derive the density function of a particular matrix form of the ratio and show that its cumulative distribution function can be expressed in terms of the hypergeometric function 2F1 of a matrix argument. Then we apply the holonomic gradient method for numerical evaluation of the hypergeometric function. This approach enables us to compute the power function of Roy’s maximum root test for testing the equality of two covariance matrices.

Keywords: D-modules; Equality of covariance matrices; Gröbner basis; Hypergeometric function of a matrix argument; Roy’s maximum root test; Zonal polynomial (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (3)

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DOI: 10.1016/j.jmva.2018.01.002

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