Estimation of the precision matrix of a multivariate elliptically contoured stable distribution

References

• Mittnik , S. , Paolella , M. S. and Rachev , S. 2000 . Diagnosis and treating the fat tails in financial returns data . J. Empir. Financ. , 7 : 389 – 416 .
   Google Scholar
• Carr , P. , Geman , H. , Madan , D. B. and Yor , M. 2002 . The fine structure af asset returns: An empirical investigation . J. Bus. , 75 : 305 – 322 .
   Web of Science ®Google Scholar
• Mandelbrot , B. B. 1963 . The variation of certain speculative prices . J. Bus. , 36 : 394 – 419 .
   Web of Science ®Google Scholar
• Fama , E. 1965 . The behavior of stock market prices . J. Bus. , 38 : 34 – 105 .
   Web of Science ®Google Scholar
• Rachev , S. T. and Mittnik , S. 2000 . Stable Paretian Models in Finance , New York : Wiley .
   Google Scholar
• Nolan , J. P. 2007 . Bibliography on stable distributions, processes and related topics . Available at http://academic2. american.edu/∼jpnolan/stable/StableBibliography.pdf
   Google Scholar
• Fama , E. and Roll , R. 1971 . Parameter estimates for symmetric stable distributions . J. Amer. Statist. Assoc. , 66 : 331 – 338 .
   Web of Science ®Google Scholar
• McCulloch , J. H. 1986 . Simple consistent estimators of stable distribution parameters . Commun. Stat. Simul. Comput. , 15 : 1109 – 1136 .
   Web of Science ®Google Scholar
• Press , S. J. 1972 . Estimation in univariate and multivariate stable distributions . J. Amer. Statist. Assoc. , 67 : 842 – 846 .
   Web of Science ®Google Scholar
• Koutrouvelis , I. A. 1980 . Regression type estimation of the parameters of stable laws . J. Amer. Statist. Assoc. , 75 : 918 – 928 .
   Web of Science ®Google Scholar
• DuMouchel , W. H. 1973 . On the asymptotic normality of the maximum-likelihood estimate when sampling from a stable distribution . Ann. Stat. , 1 : 948 – 957 .
   Web of Science ®Google Scholar
• Nolan , J. P. 2006 . Multivariate elliptically contoured stable distributions: Theory and estimation .
   Google Scholar
• Ravishanker , N. and Qiou , Z. 1999 . Monte Carlo EM estimation for multivariate stable distribution . Stat. Probab. Lett. , 45 : 335 – 340 .
   Web of Science ®Google Scholar
• Lombardi , M. and Veredas , D. 2009 . Indirect estimation of elliptical stable distributions . Comput. Stat. Data Anal. , 53 : 2309 – 2324 .
   Web of Science ®Google Scholar
• Kring , S. , Rachev , S. T. , Höchstötter , M. and Fabozzi , F. J. 2008 . “ Estimation of α-stable sub-Gaussian distributions for asset returns ” . In Risk Assessment: Decision in Banking and Finance , Edited by: Bol , G. , Racher , S. T. and Würth , R. 111 – 152 . Heidelberg : Physica–Verlag .
   Google Scholar
• Krishnamoorthy , K. and Gupta , A. K. 1989 . Improved minimax estimation of a normal precision matrix . Can. J. Statist. , 17 ( 1 ) : 91 – 102 .
   Web of Science ®Google Scholar
• Gupta , A. K. and Ofori-Nyarko , S. 1994 . Estimation of generalized variance, precision and covariance matrices using the Pitman nearness criterion . South Afr. Statist. J. , 28 : 1 – 16 .
   Google Scholar
• Gupta , A. K. and Ofori-Nyarko , S. 1995 . Improved estimation of generalized variance and precision . Statistics , 26 ( 2 ) : 99 – 109 .
   Web of Science ®Google Scholar
• Gupta , A. K. and Ofori-Nyarko , S. 1995 . Improved minimax estimators of normal covariance and precision matrices . Statistics , 26 ( 1 ) : 19 – 25 .
   Web of Science ®Google Scholar
• Kubokawa , T. 2005 . A revisit to estimation of the precision matrix of the Wishart distribution . J. Statist. Res. , 39 : 91 – 114 .
   Google Scholar
• Tsukuma , H. and Konno , Y. 2006 . On improved estimation of normal precision matrix and discriminant coefficients . J. Multivar. Anal. , 97 : 1477 – 1500 .
   Web of Science ®Google Scholar
• Sarr , A. and Gupta , A. K. 2009 . Estimation of the precision matrix of multivariate Kotz type model . J. Multivar. Anal. , 100 : 742 – 752 .
   Web of Science ®Google Scholar
• Samorodnitsky , G. and Taqqu , M. S. 1994 . Stable Non-Gaussian Random Processes: Stochastic Models with Infinite Variance , New York, London : Chapman & Hall .
   Google Scholar
• Gupta , A. K. and Varga , T. 1993 . Elliptically Contoured Models in Statistics , Dordrecht : Kluwer Academic Publishers .
   Google Scholar
• Anderson , T. W. , Fang , K. T. and Hsu , H. 1986 . Maximum likelihood estimates and likelihood-ratio criteria for multivariate elliptically contoured distributions . Can. J. Statist. , 14 ( 1 ) : 55 – 59 .
   Web of Science ®Google Scholar
• Dey , D. K. 1988 . Simultaneous estimation of eigenvalues . Ann. Inst. Stat. Math. , 40 : 137 – 147 .
   Web of Science ®Google Scholar
• Williams , E. J. 1977 . Some representations of stable random variables as products . Biometrika , 64 ( 1 ) : 167 – 169 .
   Web of Science ®Google Scholar
• Muirhead , R. J. 1982 . Aspects of Multivariate Statistical Theory , New York : Wiley .
   Google Scholar
• Gupta , A. K. and Nagar , D. K. 2000 . Matrix Variate Distributions , Boca Raton : Chapman and Hall/CRC .
   Google Scholar
• Chambers , J. W. , Mallows , C. L. and Stuck , B. W. 1976 . A method for simulating stable random variables . J. Amer. Statist. Assoc. , 71 : 340 – 344 .
   Web of Science ®Google Scholar