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Note on a paradox in decision-theoretic interval estimation

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  • Kabaila, Paul

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.

Suggested Citation

  • Kabaila, Paul, 2013. "Note on a paradox in decision-theoretic interval estimation," Statistics & Probability Letters, Elsevier, vol. 83(1), pages 123-126.
  • Handle: RePEc:eee:stapro:v:83:y:2013:i:1:p:123-126
    DOI: 10.1016/j.spl.2012.08.021
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. Farchione, Davide & Kabaila, Paul, 2012. "Confidence intervals in regression centred on the SCAD estimator," Statistics & Probability Letters, Elsevier, vol. 82(11), pages 1953-1960.
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