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A note on testing two-dimensional normal mean

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Summary

For the problem of testing a composite hypothesis with one-sided alternatives of the mean vector of a two-dimensional normal distribution, a characterization of similar tests is presented and an unbiased test dominating the likelihood ratio test is proposed. A sufficient condition for admissibility is given, which implies the result given by Cohen et al. (1983,Studies in Econometrics, Time Series and Multivariate Statistics, Academic Press): the admissibility of the likelihood ratio test.

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References

  1. Berger, R. L. (1982). Multiparameter hypothesis testing and acceptance sampling,Technometrics,24, 295–300.

    Article  MathSciNet  Google Scholar 

  2. Berger, R. L. and Sinclair, D. F. (1984). Testing hypotheses concerning unions of linear subspaces,J. Amer. Statist. Ass.,79, 158–163.

    Article  MathSciNet  Google Scholar 

  3. Cohen, A., Gatsonis, C. and Marden, J. I. (1983a). Hypothesis testing for marginal probability in a 2×2×2 contingency table with conditional independence,J. Amer. Statist. Ass.,78, 920–929.

    MATH  Google Scholar 

  4. Cohen, A., Gatsonis, C. and Marden, J. I. (1983b). Hypothesis tests and optimality properties in discrete multivariate analysis, inStudies in Econometrics, Time Series and Multivariate Statistics, Academic Press.

  5. Farrell, R. H. (1968). Towards a theory of generalized Bayes tests,Ann. Math. Statist.,39, 1–22.

    Article  MathSciNet  Google Scholar 

  6. Inada, K. (1978). Some bivariate tests of composite hypotheses with restricted alternatives,Rep. Fac. Sci. (Math. Phys. Chem.), Kagoshima University, No.11, 25–31.

    MathSciNet  MATH  Google Scholar 

  7. Lehmann, E. L. (1952). Testing multiparameter hypotheses,Ann. Math. Statist.,23, 541–552.

    Article  MathSciNet  Google Scholar 

  8. Lehmann, E. L. (1959).Testing Statistical Hypotheses, Wiley, New York.

    MATH  Google Scholar 

  9. Marshall, A. W. and Olkin, I. (1974). Majorization in multivariate distribution,Ann. Statist.,2, 1189–1200.

    Article  MathSciNet  Google Scholar 

  10. Sasabuchi, S. (1980). A test of a multivariate normal mean with composite hypotheses determine by linear inequality,Biometrika,67, 429–439.

    Article  MathSciNet  Google Scholar 

  11. Warrack, G. and Robertson, T. (1984). A likelihood ratio test regarding two nested but oblique order-restricted hypotheses,J. Amer. Statist. Ass.,79, 881–886.

    Article  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Kyushu University, Kyushu, Japan

    Kentaro Nomakuchi & Toshio Sakata

  2. Kumamoto University, Kumamoto, Japan

    Kentaro Nomakuchi & Toshio Sakata

Authors
  1. Kentaro Nomakuchi
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  2. Toshio Sakata
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Nomakuchi, K., Sakata, T. A note on testing two-dimensional normal mean. Ann Inst Stat Math 39, 489–495 (1987). https://doi.org/10.1007/BF02491485

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  • DOI: https://doi.org/10.1007/BF02491485

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