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The Nonexistence of Procedures with Bounded Performance Characteristics in Certain Parametric Inference Problems

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Abstract

This paper gives a condition which implies the nonexistence of parametric statistical procedures with bounded risk or error performance characteristics. Many examples for which such a condition is satisfied are considered.

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References

  • Blum, J. R. and Rosenblatt, J. (1969). Fixed precision estimation in the class of IPR distributions. Ann. Inst. Statist. Math., 21, 211–213.

    Google Scholar 

  • Chatterjee, S. K. (1991). Two-stage and multistage procedures. Handbook of Sequential Analysis (ed. B. K. Ghosh and P. K. Sen), 21–45, Marcel Dokker, New York.

    Google Scholar 

  • Glescr, L. J. and Hwang, J. T. (1987). The nonexistence of 100(1 − α)% confidence sets of finite expected diameter in errors-in-variables and related models, Ann. Statist., 15, 1351–1362.

    Google Scholar 

  • Hoeffding, W. and Wolfowitz, J. (1958). Distinguishability of sets of distributions, Ann. Math. Statist., 29, 700–718.

    Google Scholar 

  • Lehmann, E. L. (1951). Notes on the Theory of Estimation, University of California Press, Berkeley.

    Google Scholar 

  • Shuster, J. (1968). On the inverse Gaussian distribution function, J. Amer. Statist. Assoc., 63, 1514–1516.

    Google Scholar 

  • Singh, R. (1963). Existence of bounded length confidence intervals, Ann. Math. Statist., 34, 1474–1485.

    Google Scholar 

  • Stein, C. (1945). A two-sample test for a linear hypothesis whose power is independent of the variance, Ann. Math. Statist., 16, 243–258.

    Google Scholar 

  • Takada, Y. (1986). Non-existence of fixed sample size procedures for scale families, Sequenlial Anal., 5, 93–101.

    Google Scholar 

  • Takada, Y. (1988). Two-stage procedures for a multivariate normal distribution, Kumamoto J. Math., 1, 1–8.

    Google Scholar 

  • Zacks, S. (1971). The Theory of Statistical Inference, Wiley, New York.

    Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, Kumamoto University, Kumamoto, 860-0862, Japan

    Yoshikazu Takada

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  1. Yoshikazu Takada
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Takada, Y. The Nonexistence of Procedures with Bounded Performance Characteristics in Certain Parametric Inference Problems. Annals of the Institute of Statistical Mathematics 50, 325–335 (1998). https://doi.org/10.1023/A:1003447316747

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  • DOI: https://doi.org/10.1023/A:1003447316747

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