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

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  • 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
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    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. 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.
    5. Tetenov, Aleksey, 2012. "Statistical treatment choice based on asymmetric minimax regret criteria," Journal of Econometrics, Elsevier, vol. 166(1), pages 157-165.
    6. Charles F. Manski, 2004. "Statistical Treatment Rules for Heterogeneous Populations," Econometrica, Econometric Society, vol. 72(4), pages 1221-1246, July.
    7. Marzena Rostek, 2010. "Quantile Maximization in Decision Theory ," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 77(1), pages 339-371.
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    Citations

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    Cited by:

    1. Thomas M. Russell, 2020. "Policy Transforms and Learning Optimal Policies," Papers 2012.11046, arXiv.org.
    2. Charles F. Manski, 2019. "Statistical inference for statistical decisions," Papers 1909.06853, arXiv.org.
    3. Toru Kitagawa & Sokbae Lee & Chen Qiu, 2022. "Treatment Choice with Nonlinear Regret," Papers 2205.08586, arXiv.org, revised Feb 2024.
    4. 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.
    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.

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    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

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