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ELEVEN - Tests needed for a Recommendation


  • Karl Schlag


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

    1. Stoye, Jörg, 2009. "Minimax regret treatment choice with finite samples," Journal of Econometrics, Elsevier, vol. 151(1), pages 70-81, July.
    2. 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.
    3. Charles F. Manski, 2004. "Statistical Treatment Rules for Heterogeneous Populations," Econometrica, Econometric Society, vol. 72(4), pages 1221-1246, July.
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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. 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.
    4. Keisuke Hirano & Jack R. Porter, 2012. "Impossibility Results for Nondifferentiable Functionals," Econometrica, Econometric Society, vol. 80(4), pages 1769-1790, July.
    5. Otsu, Taisuke, 2008. "Large deviation asymptotics for statistical treatment rules," Economics Letters, Elsevier, vol. 101(1), pages 53-56, October.
    6. Karl H. Schlag, 2006. "Designing Non-Parametric Estimates and Tests for Means," Economics Working Papers ECO2006/26, European University Institute.

    More about this item


    statistical decision making; treatment response rule; binomial average rule;

    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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