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UMVU estimation of the ratio of powers of normal generalized variances under correlation

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  • Iliopoulos, George

Abstract

We consider estimation of the ratio of arbitrary powers of two normal generalized variances based on two correlated random samples. First, the result of Iliopoulos [Decision theoretic estimation of the ratio of variances in a bivariate normal distribution, Ann. Inst. Statist. Math. 53 (2001) 436-446] on UMVU estimation of the ratio of variances in a bivariate normal distribution is extended to the case of the ratio of any powers of the two variances. Motivated by these estimators' forms we derive the UMVU estimator in the multivariate case. We show that it is proportional to the ratio of the corresponding powers of the two sample generalized variances multiplied by a function of the sample canonical correlations. The mean squared errors of the derived UMVU estimator and the maximum likelihood estimator are compared via simulation for some special cases.

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  • 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.
    • Handle: RePEc:eee:jmvana:v:99:y:2008:i:6:p:1051-1069
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    References listed on IDEAS

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    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. Peña, Daniel & Rodríguez, Julio, 2003. "Descriptive measures of multivariate scatter and linear dependence," Journal of Multivariate Analysis, Elsevier, vol. 85(2), pages 361-374, May.
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    4. Tatsuya Kubokawa & Yoshihiko Konno, 1990. "Estimating the covariance matrix and the generalized variance under a symmetric loss," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 42(2), pages 331-343, June.
    5. 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.
    6. Ram Tripathi & Ramesh Gupta & John Gurland, 1994. "Estimation of parameters in the beta binomial model," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 46(2), pages 317-331, June.
    7. SenGupta, Ashis, 1987. "Tests for standardized generalized variances of multivariate normal populations of possibly different dimensions," Journal of Multivariate Analysis, Elsevier, vol. 23(2), pages 209-219, December.
    8. Ghosh M. & Sinha B. K., 1987. "Inadmissibility Of The Best Equivariant Estimators Of The Variance-Covariance Matrix, The Precision Matrix, And The Generalized Variance Under Entropy Loss," Statistics & Risk Modeling, De Gruyter, vol. 5(3-4), pages 201-228, April.
    9. Sarkar, Sanat K., 1989. "On improving the shortest length confidence interval for the generalized variance," Journal of Multivariate Analysis, Elsevier, vol. 31(1), pages 136-147, October.
    10. Sanat Sarkar, 1991. "Stein-type improvements of confidence intervals for the generalized variance," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 43(2), pages 369-375, June.
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    Cited by:

    1. Ali Jafari, 2012. "Inferences on the ratio of two generalized variances: independent and correlated cases," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 21(3), pages 297-314, August.
    2. Kokonendji, Célestin C. & Puig, Pedro, 2018. "Fisher dispersion index for multivariate count distributions: A review and a new proposal," Journal of Multivariate Analysis, Elsevier, vol. 165(C), pages 180-193.

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