Abstract
In this paper, the problem of estimating the precision matrix of a multivariate Pearson type II-model is considered. A new class of estimators is proposed. Moreover, the risk functions of the usual and the proposed estimators are explicitly derived. It is shown that the proposed estimator dominates the MLE and the unbiased estimator, under the quadratic loss function. A simulation study is carried out and confirms these results. Improved estimator of tr (Σ −1) is also obtained.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Anderson TW, Fang KT (1982) On the theory of multivariate elliptically contoured distributions and their applications. Technical Report 54. Department of Statistics, Stanford University, California. (Reprinted in Fang and Anderson 1990)
Anderson TW, Fang KT and Hsu H (1986). Maximum likelihood estimates and likelihood-ratio criteria for multivariate elliptically contoured distributions. Can J Stat 14(1): 55–59
Dey DK (1988). Simultaneous estimation of eigenvalues. Ann Inst Stat Math 40: 137–147
Efron B and Morris C (1976). Multivariate empirical Bayes and estimation of covariance matrices. Ann Stat 4: 22–32
Fang KT and Anderson TW (1990). Statistical inference in elliptically contoured and related distributions. Allerton Press, New York
Fang KT and Wang Y (1994). Number-theoretic methods in statistics. Chapman & Hall, London
Fang KT, Kotz S and Ng KW (1990). Symmetric multivariate and related distributions. Chapman & Hall, London
Gupta AK and Varga T (1993). Elliptically contoured models in statistics. Kluwer, Dordrecht
Gupta AK and Nagar DK (2000). Matrix variate distributions. Chapman & Hall/CRC, Boca Raton
Haff LR (1979). Estimation of the inverse covariance matrix: random mixtures of the inverse Wishart matrix and the identity. Ann Stat 7: 1264–1276
Joarder AH (1997). On the characteristic function of the multivariate Pearson type II distribution. J Info Opt Sci 18(1): 177–182
Joarder AH and Ahmed SE (1998). Estimation of the scale matrix of a class of elliptical distributions. Metrika 48: 149–160
Johnson ME (1987). Multivariate statistical simulation. Wiley, New York
Kano Y (1994). Consistency properties of elliptical probability density functions. J Multivar Anal 51: 139–147
Kotz S (1975) Multivariate distributions at a cross-road. In: Statistical distributions in scientific work, vol~1. Reidel, Dordrecht, pp 247–270
Krishnamoorthy K and Gupta AK (1989). Improved minimax estimation of a normal precision matrix. Can J Stat 17: 91–102
Kubokawa T (2005). A revisit to estimation of the precision matrix of the Wishart distribution. J Stat Res 39: 91–114
Pal N (1993). Estimating the normal dispersion matrix and the precision matrix from a decision-theoretic point of view. Stat Pap 34: 1–26
Tsukuma H (2005). Estimating the inverse matrix of scale parameters in an elliptically contoured distribution. J Jpn Stat Soc 35(1): 21–39
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Sarr, A., Gupta, A.K. & Joarder, A.H. Estimation of the precision matrix of multivariate Pearson type II model. Metrika 69, 31–44 (2009). https://doi.org/10.1007/s00184-008-0172-9
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00184-008-0172-9