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Hodges-Lehmann optimality of tests


  • Kallenberg, Wilbert C. M.
  • Kourouklis, Stavros


At several places in the literature there are indications that many tests are optimal in the sense of Hodges-Lehmann efficiency. It is argued here that shrinkage of the acceptance regions of the tests to the null set in a coarse way is already enough to ensure optimality. This type of argument can be used to show optimality of e.g. Kolmogorov-Smirnov tests, Cramer-von Mises tests, and likelihood ratio tests and many other tests in exponential families. AMS 1980 Subject Classifications: Primary 62G20; Secondary 62F05, 60F10

Suggested Citation

  • Kallenberg, Wilbert C. M. & Kourouklis, Stavros, 1992. "Hodges-Lehmann optimality of tests," Statistics & Probability Letters, Elsevier, vol. 14(1), pages 31-38, May.
  • Handle: RePEc:eee:stapro:v:14:y:1992:i:1:p:31-38

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    References listed on IDEAS

    1. Satorra, Albert & Bentler, Peter M., 1990. "Model conditions for asymptotic robustness in the analysis of linear relations," Computational Statistics & Data Analysis, Elsevier, vol. 10(3), pages 235-249, December.
    2. Neudecker, Heinz & Satorra, Albert, 1991. "Linear structural relations: Gradient and Hessian of the fitting function," Statistics & Probability Letters, Elsevier, vol. 11(1), pages 57-61, January.
    3. Albert Satorra, 1991. "Asymptotic robust inferences in the analysis of mean and covariance structures," Economics Working Papers 3, Department of Economics and Business, Universitat Pompeu Fabra.
    4. Robert Jennrich, 1987. "Tableau algorithms for factor analysis by instrumental variable methods," Psychometrika, Springer;The Psychometric Society, vol. 52(3), pages 469-476, September.
    5. Albert Satorra, 1989. "Alternative test criteria in covariance structure analysis: A unified approach," Psychometrika, Springer;The Psychometric Society, vol. 54(1), pages 131-151, March.
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    Cited by:

    1. 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.
    2. Canay, Ivan A. & Otsu, Taisuke, 2012. "Hodges–Lehmann optimality for testing moment conditions," Journal of Econometrics, Elsevier, vol. 171(1), pages 45-53.


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