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On improving the shortest length confidence interval for the generalized variance

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  • Sarkar, Sanat K.

Abstract

A multivariate extension of Cohen's (1972, J. Amer. Statist. Assoc. 67 382-387) result on interval estimation of normal variance is made in this article. Based on independent random matrices X : p - m and S : p - p distributed, respectively, as Npm([mu], [Sigma] [circle times operator] Im) and Wp(n, [Sigma]) with [mu] unknown and n >= p, the problem of obtaining confidence interval for [Sigma] is considered. The shortest length invariant confidence interval is obtained and is shown to be improved by some other interval estimators. Some new properties of the noncentral and central distributions of sample generalized variance have been proved for this purpose.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:jmvana:v:31:y:1989:i:1:p:136-147
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    Citations

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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. 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.
    3. 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.
    4. Constantinos Petropoulos & Stavros Kourouklis, 2012. "New classes of improved confidence intervals for the variance of a normal distribution," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 75(4), pages 491-506, May.
    5. Tatsuya Kubokawa & M. S. Srivastava, 1999. ""Estimating the Covariance Matrix: A New Approach", June 1999," CIRJE F-Series CIRJE-F-52, CIRJE, Faculty of Economics, University of Tokyo.
    6. 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.
    7. Dariush Najarzadeh, 2019. "Testing equality of standardized generalized variances of k multivariate normal populations with arbitrary dimensions," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 28(4), pages 593-623, December.

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