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Testing for affine equivalence of elliptically symmetric distributions

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  • Gupta, A. K.
  • Henze, N.
  • Klar, B.

Abstract

Let X and Y be d-dimensional random vectors having elliptically symmetric distributions. Call X and Y affinely equivalent if Y has the same distribution as AX+b for some nonsingular dxd-matrix A and some . This paper studies a class of affine invariant tests for affine equivalence under certain moment restrictions. The test statistics are measures of discrepancy between the empirical distributions of the norm of suitably standardized data.

Suggested Citation

  • Gupta, A. K. & Henze, N. & Klar, B., 2004. "Testing for affine equivalence of elliptically symmetric distributions," Journal of Multivariate Analysis, Elsevier, vol. 88(2), pages 222-242, February.
    • Handle: RePEc:eee:jmvana:v:88:y:2004:i:2:p:222-242
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    References listed on IDEAS

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    1. Henze, Norbert & Wagner, Thorsten, 1997. "A New Approach to the BHEP Tests for Multivariate Normality," Journal of Multivariate Analysis, Elsevier, vol. 62(1), pages 1-23, July.
    2. Kundu, Subrata & Majumdar, Suman & Mukherjee, Kanchan, 2000. "Central Limit Theorems revisited," Statistics & Probability Letters, Elsevier, vol. 47(3), pages 265-275, April.
    3. Anderson, N. H. & Hall, P. & Titterington, D. M., 1994. "Two-Sample Test Statistics for Measuring Discrepancies Between Two Multivariate Probability Density Functions Using Kernel-Based Density Estimates," Journal of Multivariate Analysis, Elsevier, vol. 50(1), pages 41-54, July.
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    Cited by:

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    2. Cousido-Rocha, Marta & de Uña-Álvarez, Jacobo & Hart, Jeffrey D., 2019. "A two-sample test for the equality of univariate marginal distributions for high-dimensional data," Journal of Multivariate Analysis, Elsevier, vol. 174(C).
    3. Chen, Feifei & Meintanis, Simos G. & Zhu, Lixing, 2019. "On some characterizations and multidimensional criteria for testing homogeneity, symmetry and independence," Journal of Multivariate Analysis, Elsevier, vol. 173(C), pages 125-144.

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