Exact distributional computations for Roy's statistic and the largest eigenvalue of a Wishart distribution

Authors:
Ronald W. Butler;Robert L. Paige
Affiliations:
Department of Statistical Sciences, Southern Methodist University, Dallas, USA 75275;Department of Mathematics and Statistics, Missouri University of Science and Technology, Rolla, USA 65409
Venue:
Statistics and Computing
Year:
2011

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Abstract

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.