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Remarks on statistical inference for statistical decisions

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  • Charles F. Manski

    (Institute for Fiscal Studies and Northwestern University)

Abstract

The Wald development of statistical decision theory addresses decision making with sample data. Wald's concept of a statistical decision function (SDF) embraces all mappings of the form [data => decision]. An SDF need not perform statistical inference; that is, it need not use data to draw conclusions about the true state of nature. Inference-based SDFs have the sequential form [data => inference => decision]. This paper offers remarks on the use of statistical inference in statistical decisions. Concern for tractability may provide a practical reason for study of inference-based SDFs. Another practical reason may be necessity. There often is an institutional separation between research and decision making, with researchers reporting inferences to the public. Then planners can perform the mapping [inference => decision], but they cannot perform the more basic mapping [data => decision]. The paper first addresses binary choice problems, where all SDFs may be viewed as hypothesis tests. It next considers as-if optimization, where one uses a point estimate of the true state as if the estimate is accurate. It then extend this idea to as-if decisions using set estimates of the true state, such as confidence sets.

Suggested Citation

  • 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.
    • Handle: RePEc:ifs:cemmap:06/19
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    File URL: https://www.ifs.org.uk/uploads/cemmap/wps/CWP061919.pdf
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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. 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 44/14, Institute for Fiscal Studies.
    3. 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.
    4. Charles F. Manski, 1989. "Anatomy of the Selection Problem," Journal of Human Resources, University of Wisconsin Press, vol. 24(3), pages 343-360.
    5. Stoye, Jörg, 2009. "Minimax regret treatment choice with finite samples," Journal of Econometrics, Elsevier, vol. 151(1), pages 70-81, July.
    6. Jeff Dominitz & Charles F. Manski, 2017. "More Data or Better Data? A Statistical Decision Problem," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 84(4), pages 1583-1605.
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    Cited by:

    1. Isaiah Andrews & Jesse M. Shapiro, 2021. "A Model of Scientific Communication," Econometrica, Econometric Society, vol. 89(5), pages 2117-2142, September.

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