References
- Anderson, T. W. 2003 An introduction to multivariate statistical analysis, 3rd ed. New York, NY: John Wiley & Sons.
- Coelho, C. A. 1998. The generalized integer gamma distribution—A basis for distribution in multivariate statistics. J. Multivariate Anal., 64, 86–102.
- Coelho, C. A. 2004. The generalized near-integer Gamma distribution, a basis for “near-exact” approximations to the distributions of statistics which are the product of an number of independent Beta random variables. J. Multivariate Anal., 89, 191–218.
- Coelho, C. A., and F. J. Marques. 2009. The advantage of decomposing elaborate hypotheses on covariance matrices into conditionally independent hypotheses in building near-exact distributions for the test statistics. Linear Algebra Appl., 430, 2592–2606.
- Coelho, C. A., and F. J. Marques. 2010. Near-exact distributions for the independence and sphericity likelihood ratio test statistics. J. Multivariate Anal., 101, 583–593.
- Coelho, C. A., and F. J. Marques. 2012. Near-exact distributions for the likelihood ratio test statistic to test equality of several variance-covariance matrices in elliptically contoured distributions. Comput. Stat., 27, 627–659.
- Coelho, C. A., B. C. Arnold, and F. J. Marques. 2010. Near-exact distributions for certain likelihood ratio test statistics. J. Stat. Theory Pract., 4, 711–725.
- Coelho, C. A., and J. T. Mexia. 2010. Product and ratio of generalized gamma-ratio random variables: Exact and near-exact distributions—Applications. Saarbrücken, Germany: LAP–Lambert Academic Publishing AG & Co. KG.
- Coelho, C. A., F. J. Marques, and B. C. Arnold. 2012. A general approach to the exact and near-exact distributions of the main likelihood ratio test statistics used in the complex multivariate normal setting. Preprint CMA #15/2011, CMA-FCT/UNL. http://www.cma.fct.unl.pt/sites/www.cma.fct.unl.pt/files/documentos/publicacoes/pdf_2011/CMA15-2011.pdf
- Conradsen, K., A. A. Nielsen, J. Schou, and H. Skiver. 2003 A test statistic in the complex Wishart distribution and its application to change detection in polarimetric SAR data. IEEE Trans. Geosci. Remote Sensing, 41, 4–19.
- Fang, C., P. R. Krishnaiah, and B. N. Nagarsenker. 1982. Asymptotic distributions of the likelihood ratio test statistics for covariance structures of the complex multivariate normal distributions, J. Multivariate Anal., 12, 597–611.
- Geiger, D., and J. Pearl. 1993. Logical and algorithmic properties of conditional independence and graphical models. Ann. Stat., 21, 2001–2021.
- Goodman, N. R. 1963. Statistical analysis based on a certain multivariate complex Gaussian distribution (an introduction). Ann. Math. Stat., 34, 152–177.
- Gupta, A. K. 1971. Distribution of Wilks’ likelihood-ratio criterion in the complex case. Ann. Inst. Stat. Math., 23, 77–87.
- Hannan, E. J. 1970. Multiple time series. New York, NY: Wiley.
- Khatri, C. G. 1965. Classical statistical analysis based on a certain multivariate complex Gaussian distribution, Ann. Math. Stat., 36, 98–114.
- Krishnaiah, P. R., J. C. Lee, and T. C. Chang. 1976. The distributions of the likelihood ratio statistics for tests of certain covariance structures of complex multivariate normal populations, Biometrika, 63, 543–549.
- Marques, F. J., C. A. Coelho, and B. C. Arnold, 2011. A general near-exact distribution theory for the most common likelihood ratio test statistics used in multivariate analysis. Test, 20, 180–203.
- Marques, F. J., and C. A. Coelho. 2012. The multi-sample independence test. AIP Conf. Proc., 1479, 1129–1132.
- Mathai, A. M. 1973. A few remarks about some recent articles on the exact distributions of multivariate test criteria: I. Ann. Inst. Stat. Math., 25, 557–566.
- Pannu, N. S., A. J. Coy, and J. Read. 2003. Application of the complex mul-tivariate normal distribution to crystallographic methods with insights into multiple isomorphous replacement phasing. Acta Crystallogr., Sect. D Biol.Crystallogr., 59, 1801–1808.
- Pillai, K. C. S., and G. M. Jouris, 1971. Some distribution problems in the multivariate complex Gaussian case. Ann. Math. Stat., 42, 517–525.
- Tang, J., and A. K. Gupta. 1986. Exact distribution of certain general test statistics in multivariate analysis. Aust. J. Stat., 28, 107–114.
- Tricomi, F. G., and A. Erdélyi. 1951. The asymptotic expansion of a ratio of Gamma functions. Pacific J. Math., 1, 133–142.
- Zyl, J. J., and F. T. Ulaby. 1990. Scattering matrix representation for simple targets. In Radar polarimetry for geoscience applications, ed. F. T. Ulaby and C. Elachi, 17–52. Norwood, MA: Artech House.
- Wooding, R. A. 1956. The multivariate distribution of complex normal variables. Biometrika, 43, 212–215.