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Tests for standardized generalized variances of multivariate normal populations of possibly different dimensions

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  • SenGupta, Ashis

Abstract

In many practical problems, one needs to compare variabilities of several multidimensional populations. The concept of standardized generalized variance (SGV) is introduced as an extension of the concept of GV. Considering multivariate normal populations of possibly different dimensions and general covariance matrices, LRTs are derived for SGVs. The criteria turn out to be elegant multivariate analogs to those for tests for variances in the univariate cases. The null and nonnull distributions of the test criteria are deducdd in computable forms in terms of Special Functions, e.g., Pincherle'sH-function, by exploiting the theory of calculus of residues (Mathai and Saxena,Ann. Math. Statist.40, 1439-1448).

Suggested Citation

  • 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.
    • Handle: RePEc:eee:jmvana:v:23:y:1987:i:2:p:209-219
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    Citations

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    Cited by:

    1. Pronzato, Luc & Wynn, Henry P. & Zhigljavsky, Anatoly A., 2018. "Simplicial variances, potentials and Mahalanobis distances," Journal of Multivariate Analysis, Elsevier, vol. 168(C), pages 276-289.
    2. 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.
    3. Bhandary, Madhusudan, 1996. "Test for generalized variance in signal processing," Statistics & Probability Letters, Elsevier, vol. 27(2), pages 155-162, April.
    4. 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.
    5. Grace Weishi Gu & Zachary R. Stangebye, 2023. "Costly Information And Sovereign Risk," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 64(4), pages 1397-1429, November.
    6. Ashis SenGupta & Hon Keung Tony Ng, 2011. "Nonparametric test for the homogeneity of the overall variability," Journal of Applied Statistics, Taylor & Francis Journals, vol. 38(9), pages 1751-1768, September.
    7. 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.

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