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

Statistics and Computing

Volumn 21, Issue 2, 2011, Pages 147-157

  Butler, Ronald W ^a   Paige, Robert L ^b  

^a SOUTHERN METHODIST UNIVERSITY   (United States)

^b MISSOURI UNIVERSITY OF SCIENCE AND TECHNOLOGY   (United States)

Author keywords

Convergence acceleration; Largest eigenvalue of a Wishart; Roy's test

Indexed keywords

EID: 79951551257     PISSN: 09603174     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11222-009-9154-7     Document Type: Article

References (26)

1. Abramowitz, M., Stegun, I. A.: Handbook of Mathematical Functions, 9th edn. Dover, New York (1970).
2. Aitken, A.: On Bernoulli's numerical solution of algebraic equations. Proc. R. Soc. Edinb. 46, 289-305 (1926).
3. Butler, R. W.: Saddlepoint Approximations with Applications. Cambridge University Press, Cambridge (2007).
4. Butler, R. W., Wood, A. T. A.: Laplace approximation for hypergeometric functions of matrix argument. Ann. Stat. 30, 1155-1177 (2002).
5. Butler, R. W., Wood, A. T. A.: Approximation of power in multivariate analysis. Stat. Comput. 15, 281-287 (2005).
6. Chapra, S. C.: Applied Numerical Methods with MATLAB for Engineers and Scientists. McGraw-Hill, New York (2004).
7. Clark, W. D., Gray, H. L., Adams, J. E.: A note on the T-transformation of Lubkin. J. Res. Natl. Bur. Stand. B Math. Sci. 73, 25-29 (1969).
8. Cohen, H., Villegas, F. R., Zaigler, D.: Convergence acceleration of alternating series. Exp. Math. 9, 3-12 (2000).
9. Constantine, A. G.: Some noncentral distribution problems in multivariate analysis. Ann. Math. Stat. 34, 1270-1285 (1963).
10. Goodwin, E. T. (ed.): Modern Computing Methods, 2nd edn. Philosophical Library, New York (1961).
11. Gupta, R. D., Richards, D. S. P.: Hypergeometric functions of scalar matrix argument are expressible in terms of classical hypergeometric functions. SIAM J. Math. Anal. 16, 852-858 (1985).
12. Johnson, N. L., Kotz, S.: Continuous Multivariate Distributions. Wiley, New York (1972).
13. Johnstone, I. M.: On the distribution of the largest eigenvalue in principal components analysis. Ann. Stat. 29, 295-327 (2001).
14. Johnstone, I. M.: Multivariate analysis and Jacobi ensembles: largest eigenvalue, Tracy-Widom limits and rates of convergence. Ann. Stat. 36, 2638-2716 (2008).
15. Johnstone, I. M.: Approximate null distribution of the largest root in multivariate analysis. Ann. Appl. Stat. 3 (2009, to appear).
16. Knopp, K.: Theory and Application of Infinite Series. Dover, New York (1990).
17. Kres, H.: Statistical Tables for Multivariate Analysis. Springer, New York (1983).
18. Maple 11: Maplesoft, a division of Waterloo Maple Inc., Waterloo, Ontario (2007).
19. Muirhead, R. J.: Aspects of Multivariate Statistical Theory. Wiley, New York (1982).
20. Nanda, D. N.: J. Indian Soc. Agric. Stat. 3, 175-177 (1951).
21. Pillai, K. C. S.: On the distribution of the largest or the smallest root of a matrix in multivariate analysis. Biometrika 43, 122-127 (1956).
22. Pillai, K. C. S.: On the distribution of the largest characteristic root of a matrix in multivariate analysis. Biometrika 52, 405-414 (1965).
23. Press, W. H., Teukolsky, S. A., Vetterling, W. T., Flannery, B. P.: Numerical Recipes in FORTRAN 77: The Art of Scientific Computing, 2nd edn. Cambridge University Press, Cambridge (1992).
24. Roy, S. N.: The individual sampling distribution of the maximum, the minimum, and any intermediate of the p statistics on the null hypothesis. Sankhyà 8, 133-158 (1945).
25. Scheid, F.: Schaum's Outline of Theory and Problems of Numerical Analysis, 2nd edn. McGraw-Hill, New York (1989).
26. Sugiyama, T.: Distribution of the largest latent root and the smallest latent root of the generalized B statistic and F statistic in multivariate analysis. Ann. Math. Stat. 38, 1152-1159 (1967).