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On fixed-length confidence intervals for a bounded normal mean

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  • Drees, Holger

Abstract

Consider the problem of estimating the mean of a single normal random variable when the mean is known to be bounded. We establish the minimax affine estimator under zero-one loss and discuss minimal fixed-length affine confidence intervals. Moreover, the minimal length of arbitrary fixed-size confidence intervals is described and the maximal loss of efficiency caused by the restriction to affine estimators is determined.

Suggested Citation

  • Drees, Holger, 1999. "On fixed-length confidence intervals for a bounded normal mean," Statistics & Probability Letters, Elsevier, vol. 44(4), pages 399-404, October.
    • Handle: RePEc:eee:stapro:v:44:y:1999:i:4:p:399-404
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    References listed on IDEAS

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    1. Stark, Philip B., 1992. "Affine minimax confidence intervals for a bounded normal mean," Statistics & Probability Letters, Elsevier, vol. 13(1), pages 39-44, January.
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    Cited by:

    1. Timothy B. Armstrong & Michal Kolesár, 2021. "Finite‐Sample Optimal Estimation and Inference on Average Treatment Effects Under Unconfoundedness," Econometrica, Econometric Society, vol. 89(3), pages 1141-1177, May.
    2. Timothy B. Armstrong & Michal Kolesár, 2018. "Optimal Inference in a Class of Regression Models," Econometrica, Econometric Society, vol. 86(2), pages 655-683, March.
    3. Timothy B. Armstrong & Michal Kolesár, 2017. "Finite-Sample Optimal Estimation and Inference on Average Treatment Effects Under Unconfoundedness," Cowles Foundation Discussion Papers 3015, Cowles Foundation for Research in Economics, Yale University.

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