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ELEVEN - Tests needed for a Recommendation

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  • Karl Schlag

Abstract

A decision maker has to recommend a treatment, knows that any outcome will be in [0; 1] but only has minimal information about the likelihood of outcomes (there is no prior). The decision maker can design a finite number of experiments in which treatments are tested. For the case of two treatments we present a rule for designing experiments and making a recommendation that attains minimax regret and can thus ensure a given maximal error with the minimal number of tests. 11 tests are needed under the so-called binomial average rule to limit the error to 5%. We also consider the setting where there is covariate information to then identify minimax regret behavior and drastically reduce the number of tests needed to attain a given maximal error as compared to the literature (over 200 to 22 given two covariates). We extend the binomial average rule to more than two treatments and use it to derive a bound on minimax regret.

Suggested Citation

  • Karl Schlag, 2006. "ELEVEN - Tests needed for a Recommendation," Economics Working Papers ECO2006/2, European University Institute.
    • Handle: RePEc:eui:euiwps:eco2006/2
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    References listed on IDEAS

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    1. Charles F. Manski, 2004. "Statistical Treatment Rules for Heterogeneous Populations," Econometrica, Econometric Society, vol. 72(4), pages 1221-1246, July.
    2. Stoye, Jörg, 2009. "Minimax regret treatment choice with finite samples," Journal of Econometrics, Elsevier, vol. 151(1), pages 70-81, July.
    3. Schlag, Karl H., 1998. "Why Imitate, and If So, How?, : A Boundedly Rational Approach to Multi-armed Bandits," Journal of Economic Theory, Elsevier, vol. 78(1), pages 130-156, January.
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    Citations

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    Cited by:

    1. Charles F. Manski, 2017. "Improving Clinical Guidelines and Decisions under Uncertainty," NBER Working Papers 23915, National Bureau of Economic Research, Inc.
    2. Karl H. Schlag, 2007. "Distribution-Free Learning," Economics Working Papers ECO2007/01, European University Institute.
    3. Charles F. Manski, 2019. "Treatment Choice With Trial Data: Statistical Decision Theory Should Supplant Hypothesis Testing," The American Statistician, Taylor & Francis Journals, vol. 73(S1), pages 296-304, March.
    4. Karl H. Schlag, 2007. "How to Attain Minimax Risk with Applications to Distribution-Free Nonparametric Estimation and Testing," Economics Working Papers ECO2007/04, European University Institute.
    5. Keisuke Hirano & Jack R. Porter, 2012. "Impossibility Results for Nondifferentiable Functionals," Econometrica, Econometric Society, vol. 80(4), pages 1769-1790, July.
    6. Toru Kitagawa & Sokbae Lee & Chen Qiu, 2022. "Treatment Choice with Nonlinear Regret," Papers 2205.08586, arXiv.org, revised Oct 2024.
    7. Karl H. Schlag, 2006. "Designing Non-Parametric Estimates and Tests for Means," Economics Working Papers ECO2006/26, European University Institute.
    8. Charles F. Manski & Aleksey Tetenov, 2015. "Clinical trial design enabling epsilon-optimal treatment rules," Carlo Alberto Notebooks 430, Collegio Carlo Alberto.
    9. Charles F. Manski, 2018. "Reasonable patient care under uncertainty," Health Economics, John Wiley & Sons, Ltd., vol. 27(10), pages 1397-1421, October.
    10. Toru Kitagawa & Hugo Lopez & Jeff Rowley, 2022. "Stochastic Treatment Choice with Empirical Welfare Updating," Papers 2211.01537, arXiv.org, revised Feb 2023.
    11. Charles F. Manski & Aleksey Tetenov, 2015. "Clinical trial design enabling ε-optimal treatment rules," CeMMAP working papers 60/15, Institute for Fiscal Studies.
    12. Schlag, Karl H. & Zapechelnyuk, Andriy, 2021. "Robust sequential search," Theoretical Economics, Econometric Society, vol. 16(4), November.
    13. Otsu, Taisuke, 2008. "Large deviation asymptotics for statistical treatment rules," Economics Letters, Elsevier, vol. 101(1), pages 53-56, October.

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    Keywords

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    JEL classification:

    • C79 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Other
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design

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