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Note on a paradox in decision-theoretic interval estimation

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  • Kabaila, Paul
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    Abstract

    Casella, Hwang and Robert, Statistica Sinica, 1993, consider a loss function that is a linear combination of the interval length and the indicator function that this interval includes the parameter of interest. They show that this leads to a confidence interval for the normal mean with paradoxical behavior. We show that a simple modification of this loss function removes this behavior.

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    Bibliographic Info

    Article provided by Elsevier in its journal Statistics & Probability Letters.

    Volume (Year): 83 (2013)
    Issue (Month): 1 ()
    Pages: 123-126

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    Handle: RePEc:eee:stapro:v:83:y:2013:i:1:p:123-126

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    Related research

    Keywords: Bayes’ rule; Confidence interval; Decision theory; Interval estimator;

    References

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    1. Farchione, Davide & Kabaila, Paul, 2012. "Confidence intervals in regression centred on the SCAD estimator," Statistics & Probability Letters, Elsevier, vol. 82(11), pages 1953-1960.
    2. Farchione, David & Kabaila, Paul, 2008. "Confidence intervals for the normal mean utilizing prior information," Statistics & Probability Letters, Elsevier, vol. 78(9), pages 1094-1100, July.
    3. Kabaila, Paul & Giri, Khageswor, 2009. "Large-sample confidence intervals for the treatment difference in a two-period crossover trial, utilizing prior information," Statistics & Probability Letters, Elsevier, vol. 79(5), pages 652-658, March.
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