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Asymptotics of the Optimal Confidence Region for Shift and Scale, Based on Two Order Statistics

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Using two order statistics, we construct the two-dimensional optimal strong confidence region for shift and scale parameters and study its asymptotics when the sample size tends to infinity. Also, we construct simpler confidence region asymptotically equivalent to the optimal one. The constructed confidence region is compared with similar confidence regions, based on sample mean and sample mean-square deviation.

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Author information

Authors and Affiliations

  1. Nikolay Kopernik University, Torun, Poland

    A.Yu. Zaigraev

  2. UTP University of Science and Technology, Bydgoszcz, Poland

    M. Alama-Bućko

Authors
  1. A.Yu. Zaigraev
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  2. M. Alama-Bućko
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Corresponding author

Correspondence to A.Yu. Zaigraev.

Additional information

Translated from Statisticheskie Metody Otsenivaniya i Proverki Gipotez, Vol. 19, pp. 49–65, 2006

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Zaigraev, A., Alama-Bućko, M. Asymptotics of the Optimal Confidence Region for Shift and Scale, Based on Two Order Statistics. J Math Sci 220, 763–776 (2017). https://doi.org/10.1007/s10958-016-3220-4

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  • DOI: https://doi.org/10.1007/s10958-016-3220-4

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