Exact Distributional Computations for Roy's Statistic and the Largest Eigenvalue of a Wishart Distribution
Computational expressions for the exact CDF of Roy's test statistic in MANOVA and the largest eigenvalue of a Wishart matrix are derived based upon their Pfaffian representations given in Gupta and Richards (SIAM J. Math. Anal. 16:852-858, 1985). These expressions allow computations to proceed until a prespecified degree of accuracy is achieved. For both distributions, convergence acceleration methods are used to compute CDF values which achieve reasonably fast run times for dimensions up to 50 and error degrees of freedom as large as 100. Software that implements these computations is described and has been made available on the Web.
R. W. Butler and R. Paige, "Exact Distributional Computations for Roy's Statistic and the Largest Eigenvalue of a Wishart Distribution," Statistics and Computing, Springer Verlag, Jan 2011.
The definitive version is available at https://doi.org/10.1007/s11222-009-9154-7
Mathematics and Statistics
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