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Compact Matrix Expressions for Generalized Wald Tests of Equality of Moment Vectors,


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  • Satorra, Albert
  • Neudecker, Heinz


Asymptotic chi-squared test statistics for testing the equality of moment vectors are developed. The test statistics proposed are generalized Wald test statistics that specialize for different settings by inserting an appropriate asymptotic variance matrix of sample moments. Scaled test statistics are also considered for dealing with nonstandard conditions. The specialization will be carried out for testing the equality of multinomial populations, and the equality of variance and correlation matrices for both normal and nonnormal data. When testing the equality of correlation matrices, a scaled version of the normal theory chi-squared statistic is proven to be an asymptotically exact chi-squared statistic in the case of elliptical data.

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Article provided by Elsevier in its journal Journal of Multivariate Analysis.

Volume (Year): 63 (1997)
Issue (Month): 2 (November)
Pages: 259-276

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Handle: RePEc:eee:jmvana:v:63:y:1997:i:2:p:259-276

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Keywords: chi-squared test distribution-free ellipticity moment vectors multinomial distribution normal-theory scaled test statistic variance and correlation matrices Wald test;

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  1. Donald W.K. Andrews, 1985. "Asymptotic Results for Generalized Wald Tests," Cowles Foundation Discussion Papers 761R, Cowles Foundation for Research in Economics, Yale University, revised Apr 1986.
  2. Neudecker, Heinz & Satorra, Albert, 1996. "The algebraic equality of two asymptotic tests for the hypothesis that a normal distribution has a specified correlation matrix," Statistics & Probability Letters, Elsevier, vol. 30(2), pages 99-103, October.
  3. Wilson, Jeffrey R & Koehler, Kenneth J, 1991. "Hierarchical Models for Cross-Classified Overdispersed Multinomial Data," Journal of Business & Economic Statistics, American Statistical Association, vol. 9(1), pages 103-10, January.
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