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A problem of minimax estimation with directional information

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  • Ferguson, Thomas S.

Abstract

This problem is in the area of minimax selection of experiments. Nature chooses a number [theta] in the closed interval [-1, 1]. The statistician chooses a number y in the same interval (an experiment) and is informed whether [theta] y. Based on this information, the statistician then estimates [theta] with squared error loss. The minimax solution of this problem is found. The minimax value is 1/(2e). The least favorable distribution involves the truncated t-distribution with two degrees of freedom. The minimax choice of experiment involves the truncated t-distribution with zero degrees of freedom.

Suggested Citation

  • Ferguson, Thomas S., 1996. "A problem of minimax estimation with directional information," Statistics & Probability Letters, Elsevier, vol. 26(3), pages 205-211, February.
    • Handle: RePEc:eee:stapro:v:26:y:1996:i:3:p:205-211
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    References listed on IDEAS

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    1. Donald A. Berry & Roy F. Mensch, 1986. "Discrete Search with Directional Information," Operations Research, INFORMS, vol. 34(3), pages 470-477, June.
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    Cited by:

    1. Hassin, Refael & Sarid, Anna, 2018. "Operations research applications of dichotomous search," European Journal of Operational Research, Elsevier, vol. 265(3), pages 795-812.

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