Exact Distributional Computations for Roy's Statistic and the Largest Eigenvalue of a Wishart Distribution

Author

Ronald W. Butler
Robert Paige L., Missouri University of Science and TechnologyFollow

Editor(s)

Girolami, Mark

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.

Recommended Citation

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

Department(s)

Mathematics and Statistics

International Standard Serial Number (ISSN)

0960-3174

Document Type

Article - Journal

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 2011 Springer Verlag, All rights reserved.

Publication Date

01 Jan 2011