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Improving on the Best Affine Equivariant Estimator of the Ratio of Generalized Variances

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  • Iliopoulos, George
  • Kourouklis, Stavros

Abstract

We consider the problem of decision-theoretic estimation of the ratio of generalized variances of two matrix normal distributions with unknown means under a general loss function. The inadmissibility of the best affine equivariant estimator is established by exhibiting various improved estimators. In particular, under certain conditions on the loss, two classes of improved procedures based onallthe available data are presented. As a preliminary result of independent interest, an improved estimator of an arbitrary power of the generalized variance of a matrix normal distribution with an unknown mean is derived under a general strictly bowl-shaped loss.

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  • Iliopoulos, George & Kourouklis, Stavros, 1999. "Improving on the Best Affine Equivariant Estimator of the Ratio of Generalized Variances," Journal of Multivariate Analysis, Elsevier, vol. 68(2), pages 176-192, February.
    • Handle: RePEc:eee:jmvana:v:68:y:1999:i:2:p:176-192
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    References listed on IDEAS

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    1. Sinha, Bimal Kumar, 1976. "On improved estimators of the generalized variance," Journal of Multivariate Analysis, Elsevier, vol. 6(4), pages 617-625, December.
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    9. Tatsuya Kubokawa, 1994. "Double shrinkage estimation of ratio of scale parameters," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 46(1), pages 95-116, March.
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    Cited by:

    1. George Iliopoulos, 2001. "Decision Theoretic Estimation of the Ratio of Variances in a Bivariate Normal Distribution," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 53(3), pages 436-446, September.
    2. Iliopoulos G. & Kourouklis S., 2000. "Interval Estimation For The Ratio Of Scale Parameters And For Ordered Scale Parameters," Statistics & Risk Modeling, De Gruyter, vol. 18(2), pages 169-184, February.
    3. Iliopoulos, George, 2000. "A note on decision theoretic estimation of ordered parameters," Statistics & Probability Letters, Elsevier, vol. 50(1), pages 33-38, October.
    4. Constantinos Petropoulos, 2017. "Estimation of the order restricted scale parameters for two populations from the Lomax distribution," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 80(4), pages 483-502, May.
    5. Iliopoulos, George, 2008. "UMVU estimation of the ratio of powers of normal generalized variances under correlation," Journal of Multivariate Analysis, Elsevier, vol. 99(6), pages 1051-1069, July.
    6. Panayiotis Bobotas & George Iliopoulos & Stavros Kourouklis, 2012. "Estimating the ratio of two scale parameters: a simple approach," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 64(2), pages 343-357, April.

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