Graph presentations for moments of noncentral Wishart distributions and their applications

Annals of the Institute of Statistical Mathematics

Volumn 62, Issue 4, 2010, Pages 645-672

  Kuriki, Satoshi ^a,b   Numata, Yasuhide Numata ^a,b  

^a UNIVERSITY OF TOKYO   (Japan)

^b JAPAN SCIENCE AND TECHNOLOGY AGENCY   (Japan)

Author keywords

Kibble's bivariate gamma distribution; Laguerre polynomial; Noncentral Stirling number of the first kind

Indexed keywords

BIVARIATE; BIVARIATE GAMMA DISTRIBUTION; CHI-SQUARE DISTRIBUTION; DEGENERATE CASE; DIRECTED GRAPHS; EXPLICIT FORMULA; LAGUERRE POLYNOMIAL; NONCENTRAL CHI-SQUARE DISTRIBUTION; NONCENTRAL WISHART DISTRIBUTION; STIRLING NUMBER; WISHART DISTRIBUTION;

NUMBER THEORY; PROBABILITY DISTRIBUTIONS;

POLYNOMIALS;

EID: 77958072080     PISSN: 00203157     EISSN: 15729052     Source Type: Journal    
DOI: 10.1007/s10463-010-0279-4     Document Type: Conference Paper

References (20)

1. Bai, Z. D. (1999). Methodologies in spectral analysis of large dimensional random matrices: A review. Statistica Sinica, 9, 611-677.
2. Goodman, N. R. (1963). Statistical analysis based on a certain multivariate complex Gaussian distribution: An introduction. The Annals of Mathematical Statistics, 34, 152-177.
3. Graczyk, P., Letac, G., Massam, H. (2003). The complex Wishart distribution and the symmetric groups. The Annals of Statistics, 31, 287-309.
4. Graczyk, P., Letac, G., Massam, H. (2005). The hyperoctahedral group, symmetric group representations and the moments of the real Wishart distribution. Journal of Theoretical Probability, 18, 1-42.
5. Johnson, N. L., Kotz, S., Balakrishnan, N. (1995). Continuous univariate distributions (Vol. 2, 2nd ed.). New York: Wiley-Interscience.
6. Kibble, W. F. (1941). A two-variate gamma type distribution. Sankhya, 5A, 137-150.
7. Koutras, M. (1982). Noncentral Stirling numbers and some applications. Discrete Mathematics, 42, 73-89.
8. Kuriki, S.,Takemura,A. (1996).Asymptotic expansion of null distribution of likelihood ratio statistic in multiparameter exponential family to an arbitrary order. In S.Watanabe, M. Fukushima, Yu. V. Prohorov, A. N. Shiryaev (Eds.), Probability theory and mathematical statistics: Proceedings of the seventh Japan-Russia symposium (pp. 244-255). Singapore: World Scientific.
9. Letac, G., Massam, H. (2008). The noncentral Wishart as an exponential family, and its moments. Journal of Multivariate Analysis, 99, 1393-1417.
10. Lu, I.-L., Richards, D. St. P. (2001). MacMahon's master theorem, representation theory, and moments of Wishart distributions. Advances in Applied Mathematics, 27, 531-547.
11. Maiwald, D., Kraus, D. (2000). Calculation of moments of complex Wishart and complex inverse Wishart distributed matrices. IEE Proceedings Radar, Sonar & Navigation, 147, 162-168.
12. McCullagh, P. (1987). Tensor methods in statistics. London: Chapman & Hall.
13. Morris, C. N. (1982). Natural exponential families with quadratic variance functions. The Annals of Statistics, 10, 65-80.
14. Muirhead, R. J. (1982). Aspects of multivariate statistical theory. New York: Wiley.
15. Nadarajah, S., Kotz, S. (2006). Product moments of Kibble's bivariate gamma distribution. Circuits, Systems, and Signal Processing, 25, 567-570. (Pubitemid 44480302)
16. Stanley, R.P. (2000). Enumerative combinatorics (Vol. 1, 2nd ed.) Cambridge: Cambridge University Press.
17. Takemura, A. (1991). Foundations of multivariate statistical inference (in Japanese). Tokyo: Kyoritsu Shuppan.
18. Vere-Jones, D. (1988). A generalization of permanents and determinants. Linear Algebra and its Applications, 111, 119-124.
19. Wishart, J. (1928). The generalised product moment distribution in samples from a normal multivariate population. Biometrika, 20A, 32-52.
20. Withers, C., Nadarajah, S. (2006). Simple representations for Hermite polynomials. Electronics Letters, 42, 1368-1369.