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Minimax regret treatment choice with finite samples

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  • Stoye, Jörg

Abstract

This paper applies the minimax regret criterion to choice between two treatments conditional on observation of a finite sample. The analysis is based on exact small sample regret and does not use asymptotic approximations or finite-sample bounds. Core results are: (i) Minimax regret treatment rules are well approximated by empirical success rules in many cases, but differ from them significantly-both in terms of how the rules look and in terms of maximal regret incurred-for small sample sizes and certain sample designs. (ii) Absent prior cross-covariate restrictions on treatment outcomes, they prescribe inference that is completely separate across covariates, leading to no-data rules as the support of a covariate grows. I conclude by offering an assessment of these results.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Econometrics.

Volume (Year): 151 (2009)
Issue (Month): 1 (July)
Pages: 70-81

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Handle: RePEc:eee:econom:v:151:y:2009:i:1:p:70-81

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Web page: http://www.elsevier.com/locate/jeconom

Related research

Keywords: Finite sample theory Statistical decision theory Minimax regret Treatment response Treatment choice;

References

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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, 09.
  2. Stoye, J rg, 2007. "Minimax Regret Treatment Choice With Incomplete Data And Many Treatments," Econometric Theory, Cambridge University Press, vol. 23(01), pages 190-199, February.
  3. Aleksey Tetenov, 2009. "Statistical Treatment Choice Based on Asymmetric Minimax Regret Criteria," Carlo Alberto Notebooks 119, Collegio Carlo Alberto.
  4. Charles Manski, 2003. "Statistical treatment rules for heterogeneous populations," CeMMAP working papers CWP03/03, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  5. Brock,W.A., 2004. "Profiling problems with partially identified structure," Working papers 21, Wisconsin Madison - Social Systems.
  6. Manski, Charles F., 2000. "Identification problems and decisions under ambiguity: Empirical analysis of treatment response and normative analysis of treatment choice," Journal of Econometrics, Elsevier, vol. 95(2), pages 415-442, April.
  7. Manski, Charles F., 2007. "Minimax-regret treatment choice with missing outcome data," Journal of Econometrics, Elsevier, vol. 139(1), pages 105-115, July.
  8. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
  9. Jörg Stoye, 2011. "Statistical decisions under ambiguity," Theory and Decision, Springer, vol. 70(2), pages 129-148, February.
  10. Charles F. Manski, 2005. "Search Profiling with Partial Knowledge of Deterrence," NBER Working Papers 11848, National Bureau of Economic Research, Inc.
  11. Stoye, Jörg, 2011. "Axioms for minimax regret choice correspondences," Journal of Economic Theory, Elsevier, vol. 146(6), pages 2226-2251.
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Citations

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Cited by:
  1. Keisuke Hirano & Jack R. Porter, 2012. "Impossibility Results for Nondifferentiable Functionals," Econometrica, Econometric Society, vol. 80(4), pages 1769-1790, 07.
  2. Debopam Bhattacharya & Pascaline Dupas & Shin Kanaya, 2013. "Estimating the Impact of Means-tested Subsidies under Treatment Externalities with Application to Anti-Malarial Bednets," CREATES Research Papers 2013-06, School of Economics and Management, University of Aarhus.
  3. Otsu, Taisuke, 2008. "Large deviation asymptotics for statistical treatment rules," Economics Letters, Elsevier, vol. 101(1), pages 53-56, October.
  4. Kyungchul Song, 2009. "Point Decisions for Interval-Identified Parameters," PIER Working Paper Archive 09-036, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
  5. 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.
  6. Karl Schlag, 2006. "ELEVEN - Tests needed for a Recommendation," Economics Working Papers ECO2006/2, European University Institute.
  7. Timothy B. Armstrong & Shu Shen, 2013. "Inference on Optimal Treatment Assignments," Cowles Foundation Discussion Papers 1927, Cowles Foundation for Research in Economics, Yale University.
  8. Iverson, Terrence, 2013. "Minimax regret discounting," Journal of Environmental Economics and Management, Elsevier, vol. 66(3), pages 598-608.
  9. Stoye, Jörg, 2011. "Axioms for minimax regret choice correspondences," Journal of Economic Theory, Elsevier, vol. 146(6), pages 2226-2251.
  10. Bhattacharya, Debopam & Dupas, Pascaline, 2012. "Inferring welfare maximizing treatment assignment under budget constraints," Journal of Econometrics, Elsevier, vol. 167(1), pages 168-196.
  11. Charles F. Manski, 2007. "Adaptive Minimax-Regret Treatment Choice, With Application To Drug Approval," NBER Working Papers 13312, National Bureau of Economic Research, Inc.
  12. Timothy B. Armstrong & Shu Shen, 2013. "Inference on Optimal Treatment Assignments," Cowles Foundation Discussion Papers 1927R, Cowles Foundation for Research in Economics, Yale University, revised Apr 2014.
  13. Karl H. Schlag, 2006. "Designing Non-Parametric Estimates and Tests for Means," Economics Working Papers ECO2006/26, European University Institute.
  14. J. Stoye, 2009. "Charles F. Manski, Identification for Prediction and Decision (Harvard University Press 2007)," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 24(5), pages 857-862.

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