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Statistical inference for statistical decisions

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  • Charles F. Manski

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 motivates inference-based SDFs as practical procedures for decision making that may accomplish some of what Wald envisioned. The paper first addresses binary choice problems, where all SDFs may be viewed as hypothesis tests. It next considers as-if optimization, which uses a point estimate of the true state as if the estimate were accurate. It then extends this idea to as-if maximin and minimax-regret decisions, which use point estimates of some features of the true state as if they were accurate. The paper primarily uses finite-sample maximum regret to evaluate the performance of inference-based SDFs. To illustrate abstract ideas, it presents specific findings concerning treatment choice and point prediction with sample data.

Suggested Citation

  • Charles F. Manski, 2019. "Statistical inference for statistical decisions," Papers 1909.06853, arXiv.org.
    • Handle: RePEc:arx:papers:1909.06853
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    References listed on IDEAS

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    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, 1989. "Anatomy of the Selection Problem," Journal of Human Resources, University of Wisconsin Press, vol. 24(3), pages 343-360.
    3. Stoye, Jörg, 2009. "Minimax regret treatment choice with finite samples," Journal of Econometrics, Elsevier, vol. 151(1), pages 70-81, July.
    4. Toru Kitagawa & Aleksey Tetenov, 2018. "Who Should Be Treated? Empirical Welfare Maximization Methods for Treatment Choice," Econometrica, Econometric Society, vol. 86(2), pages 591-616, March.
    5. 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.
    6. Charles F. Manski & Max Tabord-Meehan, 2017. "Evaluating the maximum MSE of mean estimators with missing data," Stata Journal, StataCorp LP, vol. 17(3), pages 723-735, September.
    7. Charles F Manski, 2007. "Adaptive Minimax-Regret Treatment Choice, with Application to Drug Approval," Levine's Working Paper Archive 122247000000001404, David K. Levine.
    8. 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.
    9. 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.
    10. Manski, Charles F., 2007. "Minimax-regret treatment choice with missing outcome data," Journal of Econometrics, Elsevier, vol. 139(1), pages 105-115, July.
    11. 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.
    12. Charles F. Manski & Aleksey Tetenov, 2019. "Trial Size for Near-Optimal Choice Between Surveillance and Aggressive Treatment: Reconsidering MSLT-II," The American Statistician, Taylor & Francis Journals, vol. 73(S1), pages 305-311, March.
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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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