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Statistical treatment choice based on asymmetric minimax regret criteria

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  • Tetenov, Aleksey

Abstract

This paper studies the problem of treatment choice between a status quo treatment with a known outcome distribution and an innovation whose outcomes are observed only in a finite sample. I evaluate statistical decision rules, which are functions that map sample outcomes into the planner’s treatment choice for the population, based on regret, which is the expected welfare loss due to assigning inferior treatments. I extend previous work started by Manski (2004) that applied the minimax regret criterion to treatment choice problems by considering decision criteria that asymmetrically treat Type I regret (due to mistakenly choosing an inferior new treatment) and Type II regret (due to mistakenly rejecting a superior innovation) and derive exact finite sample solutions to these problems for experiments with normal, Bernoulli and bounded distributions of outcomes. The paper also evaluates the properties of treatment choice and sample size selection based on classical hypothesis tests and power calculations in terms of regret.

Suggested Citation

  • Tetenov, Aleksey, 2012. "Statistical treatment choice based on asymmetric minimax regret criteria," Journal of Econometrics, Elsevier, vol. 166(1), pages 157-165.
    • Handle: RePEc:eee:econom:v:166:y:2012:i:1:p:157-165
    DOI: 10.1016/j.jeconom.2011.06.013
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    References listed on IDEAS

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    1. Keisuke Hirano & Jack R. Porter, 2009. "Asymptotics for Statistical Treatment Rules," Econometrica, Econometric Society, vol. 77(5), pages 1683-1701, September.
    2. Manski Charles F, 2009. "Adaptive Partial Drug Approval: A Health Policy Proposal," The Economists' Voice, De Gruyter, vol. 6(4), pages 1-5, March.
    3. Tversky, Amos & Kahneman, Daniel, 1992. "Advances in Prospect Theory: Cumulative Representation of Uncertainty," Journal of Risk and Uncertainty, Springer, vol. 5(4), pages 297-323, October.
    4. Charles F. Manski, 2004. "Statistical Treatment Rules for Heterogeneous Populations," Econometrica, Econometric Society, vol. 72(4), pages 1221-1246, July.
    5. Manski, Charles F., 2007. "Minimax-regret treatment choice with missing outcome data," Journal of Econometrics, Elsevier, vol. 139(1), pages 105-115, July.
    6. Daniel Kahneman & Amos Tversky, 2013. "Prospect Theory: An Analysis of Decision Under Risk," World Scientific Book Chapters, in: Leonard C MacLean & William T Ziemba (ed.), HANDBOOK OF THE FUNDAMENTALS OF FINANCIAL DECISION MAKING Part I, chapter 6, pages 99-127, World Scientific Publishing Co. Pte. Ltd..
    7. Stoye, Jörg, 2007. "Minimax Regret Treatment Choice With Incomplete Data And Many Treatments," Econometric Theory, Cambridge University Press, vol. 23(1), pages 190-199, February.
    8. Stoye, Jörg, 2009. "Minimax regret treatment choice with finite samples," Journal of Econometrics, Elsevier, vol. 151(1), pages 70-81, July.
    9. Hayashi, Takashi, 2008. "Regret aversion and opportunity dependence," Journal of Economic Theory, Elsevier, vol. 139(1), pages 242-268, March.
    10. Jörg Stoye, 2011. "Statistical decisions under ambiguity," Theory and Decision, Springer, vol. 70(2), pages 129-148, February.
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    More about this item

    Keywords

    Treatment effects; Loss aversion; Statistical decision theory; Hypothesis testing;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models
    • C44 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Operations Research; Statistical Decision Theory

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