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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.

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Bibliographic Info

Paper provided by European University Institute in its series Economics Working Papers with number ECO2006/2.

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Date of creation: 2006
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Handle: RePEc:eui:euiwps:eco2006/2

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

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References

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  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. K. Schlag, 2010. "Why Imitate, and if so, How? Exploring a Model of Social Evolution," Levine's Working Paper Archive 454, David K. Levine.
  4. Charles F. Manski, 2004. "Statistical Treatment Rules for Heterogeneous Populations," Econometrica, Econometric Society, vol. 72(4), pages 1221-1246, 07.
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Cited by:
  1. Karl H. Schlag, 2006. "Designing Non-Parametric Estimates and Tests for Means," Economics Working Papers ECO2006/26, European University Institute.
  2. 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.
  3. Hirano, Keisuke & Porter, Jack, 2009. "Impossibility Results for Nondifferentiable Functionals," MPRA Paper 15990, University Library of Munich, Germany.
  4. Otsu, Taisuke, 2008. "Large deviation asymptotics for statistical treatment rules," Economics Letters, Elsevier, vol. 101(1), pages 53-56, October.
  5. Karl H. Schlag, 2007. "Distribution-Free Learning," Economics Working Papers ECO2007/01, European University Institute.

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