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Hypothesis testing and parameter estimation based onM-statistics ink samples with unequal variances

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Summary

Ink samples with unequal variances,M-tests for homogeneity ofk location parameters are proposed. The asymptoticχ 2-distributions of the test statistics and the robustness of the tests are investigated. NextM-estimators (ME’s) of parameters are discussed. Furthermore positive-part shrinkage versions (PSME’s) of theM-estimators for the location parameters are considered along with modified James-Stein estimation rule. In asymptotic distributional risks based on a special feasible loss, it is shown that the PSME’s dominate the ME’s, and preliminary test and shrinkageM-versions fork≧4.

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References

  • Anderson T (1984) An introduction to multivariate statistical analysis. Second Ed. Wiley, New York

    MATH  Google Scholar 

  • Huber P (1964) Robust estimation of a location parameter. Annals Mathematical Statistics 35:73–101

    MathSciNet  MATH  Google Scholar 

  • Jurečková J (1969) Asymptotic linearity of a rank statistic in regression parameter. Annals Mathematical Statistics 40:1889–1900

    Google Scholar 

  • Lepage Y (1977) A class of nonparametric tests for location and scale parameters. Communications Statistics Ser A 6:649–659

    Article  MathSciNet  Google Scholar 

  • Muirhead R (1982) Aspects of multivariate statistical theory. Wiley, New York

    MATH  Google Scholar 

  • Sclove S, Morris C, Radhakrishnan R (1972) Non-optimality of preliminary test estimators for the mean of a multi-variate normal distribution. Annals Mathematical Statistics 43:1481–1490

    MathSciNet  MATH  Google Scholar 

  • Sen P, Saleh A (1987) On preliminary test and shrinkageM-estimation in linear models. Annals Statistics 15:1580–1592

    MATH  MathSciNet  Google Scholar 

  • Shiraishi T (1989) Asymptotic equivalence of statistical inference based on aligned ranks and on within-block ranks. Journal Statistical Planning Inference 21:347–364

    Article  MATH  MathSciNet  Google Scholar 

  • Shiraishi T (1990)M-tests in multivariate models. Metrika 37:189–197

    MathSciNet  MATH  Google Scholar 

  • Singer J, Sen P (1985)M-methods in multivariate linear models. Journal Multivariate Analysis 17:168–184

    Article  MATH  MathSciNet  Google Scholar 

  • Stein C (1966) An approach to the recovery of interblock information in balanced incomplete block designs. In: David FN (ed) Research Papers in Statistics: Festschrift for J. Neyman. Wiley, New York, pp 351–366

    Google Scholar 

  • Welch B (1949) Further notes on Mrs. Aspin’s tables. Biometrika 36:243–246

    MathSciNet  Google Scholar 

Download references

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Authors and Affiliations

  1. Department of Mathematics, Yokohama City University, 22-2, Seto, Kanazawa-ku, 236, Yokohama, Japan

    T. Shiraishi

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  1. T. Shiraishi
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Shiraishi, T. Hypothesis testing and parameter estimation based onM-statistics ink samples with unequal variances. Metrika 38, 163–178 (1991). https://doi.org/10.1007/BF02613609

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  • DOI: https://doi.org/10.1007/BF02613609

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