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Estimation of the precision matrix of multivariate Kotz type model

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  • Sarr, Amadou
  • Gupta, Arjun K.

Abstract

In this paper, the problem of estimating the precision matrix of a multivariate Kotz type model is considered. First, using the quadratic loss function, we prove that the unbiased estimator , where denotes the sample sum of product matrix, is dominated by a better constant multiple of , denoted by . Secondly, a new class of shrinkage estimators of is proposed. Moreover, the risk functions of , and the proposed estimators are explicitly derived. It is shown that the proposed estimator dominates , under the quadratic loss function. A simulation study is carried out which confirms these results. Improved estimator of is also obtained.

Suggested Citation

  • Sarr, Amadou & Gupta, Arjun K., 2009. "Estimation of the precision matrix of multivariate Kotz type model," Journal of Multivariate Analysis, Elsevier, vol. 100(4), pages 742-752, April.
    • Handle: RePEc:eee:jmvana:v:100:y:2009:i:4:p:742-752
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    References listed on IDEAS

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    1. Haff, L. R., 1979. "An identity for the Wishart distribution with applications," Journal of Multivariate Analysis, Elsevier, vol. 9(4), pages 531-544, December.
    2. J. K. Lindsey, 1999. "Multivariate Elliptically Contoured Distributions for Repeated Measurements," Biometrics, The International Biometric Society, vol. 55(4), pages 1277-1280, December.
    3. Kano, Y., 1994. "Consistency Property of Elliptic Probability Density Functions," Journal of Multivariate Analysis, Elsevier, vol. 51(1), pages 139-147, October.
    4. Dipak Dey, 1988. "Simultaneous estimation of eigenvalues," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 40(1), pages 137-147, March.
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    Cited by:

    1. Bodnar, Taras & Gupta, Arjun K. & Parolya, Nestor, 2016. "Direct shrinkage estimation of large dimensional precision matrix," Journal of Multivariate Analysis, Elsevier, vol. 146(C), pages 223-236.
    2. Hashorva, Enkelejd, 2010. "On the residual dependence index of elliptical distributions," Statistics & Probability Letters, Elsevier, vol. 80(13-14), pages 1070-1078, July.
    3. Taras Bodnar & Arjun Gupta, 2013. "An exact test for a column of the covariance matrix based on a single observation," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 76(6), pages 847-855, August.
    4. Taras Bodnar & Arjun K. Gupta & Nestor Parolya, 2013. "Optimal Linear Shrinkage Estimator for Large Dimensional Precision Matrix," Papers 1308.0931, arXiv.org, revised Mar 2014.

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