Keywords and phrases: Kotz type distribution, Kotz-Wishart distribution, estimation, zonal polynomials, hypergeometric functions, M-Varma transform.
How to cite this article: Amadou Sarr, A generalized Wishart distribution: matrix variate Varma transform, Far East Journal of Theoretical Statistics 63(2) (2021), 51-83. DOI: 10.17654/0972086321001
This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License
References:
[1] S. Adhikari, Generalized Wishart distribution for probabilistic structural dynamics, Comput. Mech. 45 (2010), 495-511. [2] T. W. Anderson, An Introduction to Multivariate Statistical Analysis, 3rd ed., Wiley, New York, 2003. [3] J. Bai and S. Shi, Estimating high dimensional covariance matrices and its applications, Ann. Econ. Finance 12(2) (2011), 199-215. [4] A. Bellahnid and A. Sarr, Skewed Kotz distribution with application to financial stock returns, J. Stat. Theory and Practice 13(4) (2019), 1-33. doi:10.1007/s42519-019-0054-7. [5] T. Bodnar, S. Mazur and K. Podgorski, Singular inverse Wishart distribution and its application to portfolio theory, J. Multivariate Anal. 143 (2016), 314-326. [6] A. G. Constantine, Some non-central distribution problems in multivariate analysis, Ann. Math. Statist. 34 (1963), 1270-1285. [7] F. J. Caro-Lopera, G. González-Farías and N. Balakrishnan, On generalized Wishart distribution-I: Likelihood ratio test for homogeneity of the covariance matrices, Sankhya A 76 (2014), 179-194. [8] F. J. Caro-Lopera, J. A. Díaz-García and G. González-Farías, Noncentral elliptical configuration density, J. Multivariate Anal. 101(1) (2010), 32-43. [9] K. T. Fang and T. W. Anderson, Statistical Inference in Elliptically Contoured and Related Distributions, Allerton Press, New York, 1990. [10] K. T. Fang, S. Kotz and K. W. Ng, Symmetric Multivariate and Related Distributions, Chapman and Hall, London, New York, 1990. [11] K. T. Fang and Y. T. Zhang, Generalized Multivariate Analysis, Springer-Verlag, New York, 1990. [12] I. S. Gradshteyn and I. M. Ryzhik, Tables of Integrals, Series, and Products, Seventh ed., Academic Press, New York, 2007. [13] A. K. Gupta and D. K. Nagar, Matrix Variate Distributions, Chapman and Hall/CRC, Boca Raton, 2000. [14] A. K. Gupta and T. Varga, Elliptically Contoured Models in Statistics, Kluwer Academic Publishers, Dordrecht, 1993. [15] C. S. Herz, Bessel functions of matrix argument, Ann. Math. 61 (1955), 474-523. [16] A. T. James, Zonal polynomials of the real positive definite symmetric matrices, Ann. Math. 74 (1961), 456-469. [17] H. H. Kelejian and I. R. Prucha, Independent or uncorrelated disturbances in linear regression: an illustration of the difference, Econom. Lett. 19 (1985), 35-38. [18] P. Koev and A. Edelman, The efficient evaluation of the hypergeometric function of a matrix argument, Math. Comp. 75 (2006), 833-846. [19] S. Kotz, Multivariate distributions at a cross road, A Modern Course on Statistical Distributions in Scientific Work, Reidel, Dordrecht, 1975, pp. 247-270. [20] M. O. Kuismin and M. J. Sillanpaa, Estimation of covariance and precision matrix, network structure, and a view toward systems biology, WIRE’s Comput. Stat. 9 (2017), e1415. doi:10.1002/wics.1415. [21] O. Ledoit and M. Wolf, Improved estimation of the covariance matrix of stock returns with an application to portfolio selection, Journal of Empirical Finance 10 (2004b), 603-621. [22] J. K. Lindsey, Multivariate elliptically contoured distributions for repeated measurements, Biometrics 55 (1999), 1277-1280. [23] R. J. Muirhead, Aspects of Multivariate Statistical Theory, Wiley, New York, 2005. [24] S. Nadarajah, The Kotz-type distribution with applications, Statistics 37(4) (2003), 341-358. [25] F. Oberhettinger, Tables of Mellin Transforms, Springer-Verlag, Berlin, 1974. [26] A. Sarr, On a Kotz-Wishart distribution: multivariate Varma transform, 2014. arXiv:1404.4441v1. [27] A. Sarr and A. K. Gupta, Estimation of the precision matrix of multivariate Kotz type model, J. Multivariate Anal. 100 (2009), 742-752. [28] A. Sarr and A. K. Gupta, Exponential scale mixture of matrix variate Cauchy distributions, Proc. Amer. Math. Soc. 139(4) (2011), 1483-1494. [29] H. M. Srivastava, Fractional integration and inversion formulae associated with the generalized Whittaker transform, Pacific J. Math. 26 (1968), 375-377. [30] B. C. Sutradhar and M. M. Ali, A generalization of the Wishart distribution for the elliptical model and its moments for the multivariate t model, J. Multivariate Anal. 29 (1989), 155-162. [31] R. S. Varma, On a generalization of Laplace integral, Proc. Nat. Acad. Sci. India Sect. A 20 (1951), 209-216. [32] J. Wishart, Generalized product moment distribution in samples from a normal multivariate population, Biometrika 20 (1928), 32-52.
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