IDEAS home Printed from https://ideas.repec.org/p/eui/euiwps/eco2006-2.html
   My bibliography  Save this paper

ELEVEN - Tests needed for a Recommendation

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://cadmus.iue.it/dspace/bitstream/1814/3937/1/ECO2006-2.pdf
    File Function: main text
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

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

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Tetenov, Aleksey, 2012. "Statistical treatment choice based on asymmetric minimax regret criteria," Journal of Econometrics, Elsevier, vol. 166(1), pages 157-165.
    2. Manski, Charles F., 2023. "Probabilistic prediction for binary treatment choice: With focus on personalized medicine," Journal of Econometrics, Elsevier, vol. 234(2), pages 647-663.
    3. Masahiro Kato & Masaaki Imaizumi & Takuya Ishihara & Toru Kitagawa, 2023. "Asymptotically Optimal Fixed-Budget Best Arm Identification with Variance-Dependent Bounds," Papers 2302.02988, arXiv.org, revised Jul 2023.
    4. Eric Mbakop & Max Tabord‐Meehan, 2021. "Model Selection for Treatment Choice: Penalized Welfare Maximization," Econometrica, Econometric Society, vol. 89(2), pages 825-848, March.
    5. Anders Bredahl Kock & Martin Thyrsgaard, 2017. "Optimal sequential treatment allocation," Papers 1705.09952, arXiv.org, revised Aug 2018.
    6. Garbero, Alessandra & Sakos, Grayson & Cerulli, Giovanni, 2023. "Towards data-driven project design: Providing optimal treatment rules for development projects," Socio-Economic Planning Sciences, Elsevier, vol. 89(C).
    7. Timothy B. Armstrong & Shu Shen, 2013. "Inference on Optimal Treatment Assignments," Cowles Foundation Discussion Papers 1927RR, Cowles Foundation for Research in Economics, Yale University, revised Apr 2015.
    8. Firpo, Sergio & Galvao, Antonio F. & Kobus, Martyna & Parker, Thomas & Rosa-Dias, Pedro, 2020. "Loss Aversion and the Welfare Ranking of Policy Interventions," IZA Discussion Papers 13176, Institute of Labor Economics (IZA).
    9. Bhattacharya, Debopam & Dupas, Pascaline, 2012. "Inferring welfare maximizing treatment assignment under budget constraints," Journal of Econometrics, Elsevier, vol. 167(1), pages 168-196.
    10. Charles F. Manski, 2020. "Towards Reasonable Patient Care Under Uncertainty," Contemporary Economic Policy, Western Economic Association International, vol. 38(2), pages 227-245, April.
    11. Isaiah Andrews & Jesse M. Shapiro, 2021. "A Model of Scientific Communication," Econometrica, Econometric Society, vol. 89(5), pages 2117-2142, September.
    12. Charles F. Manski, 2018. "Reasonable patient care under uncertainty," Health Economics, John Wiley & Sons, Ltd., vol. 27(10), pages 1397-1421, October.
    13. Yuchen Hu & Henry Zhu & Emma Brunskill & Stefan Wager, 2024. "Minimax-Regret Sample Selection in Randomized Experiments," Papers 2403.01386, arXiv.org.
    14. Aleksey Tetenov, 2016. "An economic theory of statistical testing," CeMMAP working papers 50/16, Institute for Fiscal Studies.
    15. Kock, Anders Bredahl & Preinerstorfer, David & Veliyev, Bezirgen, 2023. "Treatment recommendation with distributional targets," Journal of Econometrics, Elsevier, vol. 234(2), pages 624-646.
    16. 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, Department of Economics and Business Economics, Aarhus University.
    17. Charles F. Manski & Aleksey Tetenov, 2014. "The Quantile Performance of Statistical Treatment Rules Using Hypothesis Tests to Allocate a Population to Two Treatments," CeMMAP working papers CWP44/14, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    18. Susan Athey & Stefan Wager, 2021. "Policy Learning With Observational Data," Econometrica, Econometric Society, vol. 89(1), pages 133-161, January.
    19. Azevedo, Eduardo M. & Mao, David & Montiel Olea, José Luis & Velez, Amilcar, 2023. "The A/B testing problem with Gaussian priors," Journal of Economic Theory, Elsevier, vol. 210(C).
    20. Shosei Sakaguchi, 2021. "Estimation of Optimal Dynamic Treatment Assignment Rules under Policy Constraints," Papers 2106.05031, arXiv.org, revised Apr 2024.

    More about this item

    Keywords

    statistical decision making; treatment response rule; binomial average rule;
    All these keywords.

    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

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eui:euiwps:eco2006/2. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Cécile Brière (email available below). General contact details of provider: https://edirc.repec.org/data/deiueit.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.