IDEAS home Printed from https://ideas.repec.org/p/cca/wpaper/361.html
   My bibliography  Save this paper

The Quantile Performance Of Statistical Treatment Rules Using Hypothesis Tests To Allocate A Population To Two Treatments

Author

Listed:
  • Charles F. Manski
  • Aleksey Tetenov

Abstract

This paper modifies the Wald development of statistical decision theory to offer new perspective on the performance of certain statistical treatment rules. We study the quantile performance of test rules, ones that use the outcomes of hypothesis tests to allocate a population to two treatments. Let lambda denote the quantile used to evaluate performance. Define a test rule to be lambda-quantile optimal if it maximizes lambda-quantile welfare in every state of nature. We show that a test rule is lambda-quantile optimal if and only if its error probabilities are less than lambda in all states where the two treatments yield different welfare. We give conditions under which lambda-quantile optimal test rules do and do not exist. We find that optimal rules exist when the state space is finite and the data enable sufficiently precise estimation of the true state. Optimal rules do not exist when the state space is connected and other regularity conditions hold. These nuanced findings differ sharply from measurement of mean performance, as mean optimal test rules generically do not exist. We present further analysis that holds when the data are real-valued and generated by a sampling distribution which satisfies the monotone-likelihood ratio (MLR) property with respect to the average treatment effect. We use the MLR property to characterize the stochastic-dominance admissibility of STRs when the data have a continuous distribution and then generate findings on the quantile admissibility of test rules.

Suggested Citation

  • Charles F. Manski & Aleksey Tetenov, 2014. "The Quantile Performance Of Statistical Treatment Rules Using Hypothesis Tests To Allocate A Population To Two Treatments," Carlo Alberto Notebooks 361, Collegio Carlo Alberto.
    • Handle: RePEc:cca:wpaper:361
    as

    Download full text from publisher

    File URL: https://www.carloalberto.org/wp-content/uploads/2018/11/no.361.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Manski, Charles F., 1986. "Ordinal Utility Models Of Decision Making Under Uncertainty," SSRI Workshop Series 292682, University of Wisconsin-Madison, Social Systems Research Institute.
    2. Stoye, Jörg, 2009. "Minimax regret treatment choice with finite samples," Journal of Econometrics, Elsevier, vol. 151(1), pages 70-81, July.
    3. Keisuke Hirano & Jack R. Porter, 2009. "Asymptotics for Statistical Treatment Rules," Econometrica, Econometric Society, vol. 77(5), pages 1683-1701, September.
    4. Charles F. Manski, 2004. "Statistical Treatment Rules for Heterogeneous Populations," Econometrica, Econometric Society, vol. 72(4), pages 1221-1246, July.
    5. Tetenov, Aleksey, 2012. "Statistical treatment choice based on asymmetric minimax regret criteria," Journal of Econometrics, Elsevier, vol. 166(1), pages 157-165.
    6. Marzena Rostek, 2010. "Quantile Maximization in Decision Theory ," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 77(1), pages 339-371.
    7. Stoye, Jörg, 2012. "Minimax regret treatment choice with covariates or with limited validity of experiments," Journal of Econometrics, Elsevier, vol. 166(1), pages 138-156.
    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. Toru Kitagawa & Sokbae Lee & Chen Qiu, 2022. "Treatment Choice with Nonlinear Regret," Papers 2205.08586, arXiv.org, revised Oct 2024.
    2. Charles F. Manski, 2019. "Remarks on statistical inference for statistical decisions," CeMMAP working papers CWP06/19, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    3. Thomas M. Russell, 2020. "Policy Transforms and Learning Optimal Policies," Papers 2012.11046, arXiv.org.
    4. Charles F. Manski, 2019. "Statistical inference for statistical decisions," Papers 1909.06853, arXiv.org.
    5. Charles F. Manski, 2021. "Econometrics for Decision Making: Building Foundations Sketched by Haavelmo and Wald," Econometrica, Econometric Society, vol. 89(6), pages 2827-2853, November.

    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. Thomas M. Russell, 2020. "Policy Transforms and Learning Optimal Policies," Papers 2012.11046, arXiv.org.
    2. Charles F. Manski & Aleksey Tetenov, 2023. "Statistical decision theory respecting stochastic dominance," The Japanese Economic Review, Springer, vol. 74(4), pages 447-469, October.
    3. Toru Kitagawa & Sokbae Lee & Chen Qiu, 2022. "Treatment Choice with Nonlinear Regret," Papers 2205.08586, arXiv.org, revised Oct 2024.
    4. 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.
    5. Eric Mbakop & Max Tabord‐Meehan, 2021. "Model Selection for Treatment Choice: Penalized Welfare Maximization," Econometrica, Econometric Society, vol. 89(2), pages 825-848, March.
    6. Susan Athey & Stefan Wager, 2021. "Policy Learning With Observational Data," Econometrica, Econometric Society, vol. 89(1), pages 133-161, January.
    7. Keisuke Hirano & Jack R. Porter, 2016. "Panel Asymptotics and Statistical Decision Theory," The Japanese Economic Review, Japanese Economic Association, vol. 67(1), pages 33-49, March.
    8. Daido Kido, 2023. "Locally Asymptotically Minimax Statistical Treatment Rules Under Partial Identification," Papers 2311.08958, arXiv.org.
    9. Anders Bredahl Kock & David Preinerstorfer, 2024. "Regularizing Discrimination in Optimal Policy Learning with Distributional Targets," Papers 2401.17909, arXiv.org.
    10. Anders Bredahl Kock & David Preinerstorfer & Bezirgen Veliyev, 2022. "Functional Sequential Treatment Allocation," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 117(539), pages 1311-1323, September.
    11. Kitagawa, Toru & Wang, Guanyi, 2023. "Who should get vaccinated? Individualized allocation of vaccines over SIR network," Journal of Econometrics, Elsevier, vol. 232(1), pages 109-131.
    12. Davide Viviano, 2019. "Policy Targeting under Network Interference," Papers 1906.10258, arXiv.org, revised Apr 2024.
    13. 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.
    14. Anders Bredahl Kock & Martin Thyrsgaard, 2017. "Optimal sequential treatment allocation," Papers 1705.09952, arXiv.org, revised Aug 2018.
    15. 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).
    16. 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.
    17. 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).
    18. Bhattacharya, Debopam & Dupas, Pascaline, 2012. "Inferring welfare maximizing treatment assignment under budget constraints," Journal of Econometrics, Elsevier, vol. 167(1), pages 168-196.
    19. Yuchen Hu & Henry Zhu & Emma Brunskill & Stefan Wager, 2024. "Minimax-Regret Sample Selection in Randomized Experiments," Papers 2403.01386, arXiv.org, revised Jun 2024.
    20. Aleksey Tetenov, 2016. "An economic theory of statistical testing," CeMMAP working papers 50/16, Institute for Fiscal Studies.

    More about this item

    Keywords

    treatment choice; quantiles; stochastic dominance; monotone likelihood ratio;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C44 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Operations Research; Statistical Decision Theory

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:cca:wpaper:361. 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: Giovanni Bert (email available below). General contact details of provider: https://edirc.repec.org/data/fccaait.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.