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Optimal sample sizes and statistical decision rules

Author

Listed:
  • Patil, Sanket

    (Economics Area, Indian Institute of Management Bangalore)

  • Salant, Yuval

    (Kellogg School of Management, Northwestern University)

Abstract
A statistical decision rule is a mapping from data to actions induced by statistical inference on the data. We characterize these rules for data that are chosen strategically in persuasion environments. A designer wishes to persuade a decision maker (DM) to take a particular action and decides how many Bernoulli experiments about a parameter of interest the DM can obtain. After obtaining these data and estimating the parameter value, the DM chooses to take the action if the estimated value exceeds some threshold. We establish that as the threshold changes, the resulting statistical decision rules in many environments are either simple majority or reverse unanimity.

Suggested Citation

  • Patil, Sanket & Salant, Yuval, 2024. "Optimal sample sizes and statistical decision rules," Theoretical Economics, Econometric Society, vol. 19(2), May.
    • Handle: RePEc:the:publsh:4840
    as

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    File URL: http://econtheory.org/ojs/index.php/te/article/viewFile/20240583/39115/1189
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    References listed on IDEAS

    as
    1. Sethi, Rajiv, 2000. "Stability of Equilibria in Games with Procedurally Rational Players," Games and Economic Behavior, Elsevier, vol. 32(1), pages 85-104, July.
    2. Sylvain Chassang & Gerard Padro I Miquel & Erik Snowberg, 2012. "Selective Trials: A Principal-Agent Approach to Randomized Controlled Experiments," American Economic Review, American Economic Association, vol. 102(4), pages 1279-1309, June.
    3. Abhijit V. Banerjee & Sylvain Chassang & Sergio Montero & Erik Snowberg, 2020. "A Theory of Experimenters: Robustness, Randomization, and Balance," American Economic Review, American Economic Association, vol. 110(4), pages 1206-1230, April.
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    Cited by:

    1. Alon, Shiri & Auster, Sarah & Gayer, Gabi & Minardi, Stefania, 2023. "Persuasion with Limited Data: A Case-Based Approach," CEPR Discussion Papers 18428, C.E.P.R. Discussion Papers.

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    More about this item

    Keywords

    Statistical inference; statistical decision rule; sample size; persuasion;
    All these keywords.

    JEL classification:

    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness
    • C90 - Mathematical and Quantitative Methods - - Design of Experiments - - - General

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