Compact matrix expressions for generalized Wald tests of equality of moment vectors
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 and appropriate asymptotic variance matrix of sample moments. Scaled test statistics are also considered for dealing with situations of non-iid sampling. 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 non-normal 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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- 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.
- 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 103-110, January.
- Heinz Neudecker & Albert Satorra, 1995.
"The algebraic equality of two asymptotic tests for the hypothesis that a normal distribution has a specified correlation matrix,"
Economics Working Papers
131, Department of Economics and Business, Universitat Pompeu Fabra.
- 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.
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