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Hotelling’s T2 tests in paired and independent survey samples: An efficiency comparison

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  • Baringhaus, Ludwig
  • Gaigall, Daniel

Abstract

Hotelling’s T2 tests in paired and independent survey samples are compared using the traditional asymptotic efficiency concepts of Hodges–Lehmann, Bahadur and Pitman, as well as through criteria based on the volumes of corresponding confidence regions. Conditions characterizing the superiority of a procedure are given in terms of population canonical correlation type coefficients. Statistical tests for checking these conditions are developed. Test statistics based on the eigenvalues of a symmetrized sample cross-covariance matrix are suggested, as well as test statistics based on sample canonical correlation type coefficients.

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  • Baringhaus, Ludwig & Gaigall, Daniel, 2017. "Hotelling’s T2 tests in paired and independent survey samples: An efficiency comparison," Journal of Multivariate Analysis, Elsevier, vol. 154(C), pages 177-198.
    • Handle: RePEc:eee:jmvana:v:154:y:2017:i:c:p:177-198
    DOI: 10.1016/j.jmva.2016.11.004
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    1. P. Groeneboom & J. Oosterhoff, 1977. "Bahadur efficiency and probabilities of large deviations," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 31(1), pages 1-24, March.
    2. Kallenberg, Wilbert C. M. & Kourouklis, Stavros, 1992. "Hodges-Lehmann optimality of tests," Statistics & Probability Letters, Elsevier, vol. 14(1), pages 31-38, May.
    3. Magnus, Jan R., 1985. "On Differentiating Eigenvalues and Eigenvectors," Econometric Theory, Cambridge University Press, vol. 1(2), pages 179-191, August.
    4. Baringhaus, Ludwig, 1987. "Asymptotic optimality of multivariate linear hypothesis tests," Journal of Multivariate Analysis, Elsevier, vol. 23(2), pages 303-311, December.
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    1. Ludwig Baringhaus & Daniel Gaigall, 2018. "Efficiency comparison of the Wilcoxon tests in paired and independent survey samples," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 81(8), pages 891-930, November.

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