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Asymptotic Comparison of MLE and UMVUE in the Case of a Truncated One-Parameter Family of Distributions

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The paper focuses on the asymptotic comparison of the maximum likelihood estimators and the uniformly minimum variance unbiased estimators (with respect to quadratic loss) for one-parameter truncation families where a sufficient statistic is either the minimum or the maximum of the sample. Easily verifiable conditions are formulated under which those asymptotic results are valid.

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References

  1. I. Barranco-Chamorro, J. L. Moreno-Rebollo, and M.T. Gomez-Gomez, “Asymptotic properties of MLE and UMVUE in one-parameter truncated distributions,” Metrika, 54, 97–110 (2001).

    Article  MathSciNet  Google Scholar 

  2. M.B. Bhatt and S.R. Patel, “Asymptotic distribution for the order statistics of a truncated one-parameter family of distributions,” Comm. Statist. Theor. Meth., 28, No. 8, 1823–1855 (1999).

    Article  MathSciNet  Google Scholar 

  3. V.V. Chichagov, “The limit distribution of unbiased estimators of integral functionals whose sufficient statistics of the unknown parameter are the minimum and the maximum,” J. Math. Sci., 127, 2091–2094 (2005).

    Article  MathSciNet  Google Scholar 

  4. E. L. Lehmann and G. Casella, Theory of Point Estimation. Second edition, Springer, Berlin (1998).

    MATH  Google Scholar 

  5. J.R. McCord, “On asymptotic moments of extreme statistics,” Ann. Math. Statist., 35, No. 4, 1738–1745 (1964).

    Article  MathSciNet  Google Scholar 

  6. R.F. Tate, “Unbiased estimation: functions of location and scale parameters,” Ann. Math. Statist., 30, 341–366 (1959).

    Article  MathSciNet  Google Scholar 

  7. V.G. Voinov and M. S. Nikulin, Unbiased Estimators and Their Applications. Vol. 1: Univariate Case, Kluwer Academic Publishers, Dordrecht (1993).

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Authors and Affiliations

  1. Perm State University, Perm, Russia

    V. V. Chichagov

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  1. V. V. Chichagov
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Correspondence to V. V. Chichagov.

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Translated from Statisticheskie Metody Otsenivaniya i Proverki Gipotez, Vol. 23, pp. 166–180, 2011

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Chichagov, V.V. Asymptotic Comparison of MLE and UMVUE in the Case of a Truncated One-Parameter Family of Distributions. J Math Sci 267, 170–179 (2022). https://doi.org/10.1007/s10958-022-06122-1

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  • DOI: https://doi.org/10.1007/s10958-022-06122-1

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