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Testing Multiple Forecasters

Author

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  • Feinberg, Yossi

    (Stanford U)

  • Stewart, Colin

    (Yale U)

Abstract

We consider a cross-calibration test of predictions by multiple potential experts in a stochastic environment. This test checks whether each expert is calibrated conditional on the predictions made by other experts. We show that this test is good in the sense that a true expert--one informed of the true distribution of the process--is guaranteed to pass the test no matter what the other potential experts do, and false experts will fail the test on all but a small (category one) set of true distributions. Furthermore, even when there is no true expert present, a test similar to cross-calibration cannot be simultaneously manipulated by multiple false experts, but at the cost of failing some true experts. In contrast, tests that allow false experts to make precise predictions can be jointly manipulated.

Suggested Citation

  • Feinberg, Yossi & Stewart, Colin, 2007. "Testing Multiple Forecasters," Research Papers 1957, Stanford University, Graduate School of Business.
    • Handle: RePEc:ecl:stabus:1957
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    References listed on IDEAS

    as
    1. Nabil I. Al-Najjar & Jonathan Weinstein, 2008. "Comparative Testing of Experts," Econometrica, Econometric Society, vol. 76(3), pages 541-559, May.
    2. Kalai, Ehud & Lehrer, Ehud & Smorodinsky, Rann, 1999. "Calibrated Forecasting and Merging," Games and Economic Behavior, Elsevier, vol. 29(1-2), pages 151-169, October.
    3. Fudenberg, Drew & Levine, David K., 1999. "Conditional Universal Consistency," Games and Economic Behavior, Elsevier, vol. 29(1-2), pages 104-130, October.
    4. Alvaro Sandroni, 2003. "The reproducible properties of correct forecasts," International Journal of Game Theory, Springer;Game Theory Society, vol. 32(1), pages 151-159, December.
    5. Eddie Dekel & Yossi Feinberg, 2006. "Non-Bayesian Testing of a Stochastic Prediction," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 73(4), pages 893-906.
    6. Wojciech Olszewski & Alvaro Sandroni, 2006. "Strategic Manipulation of Empirical Tests," Discussion Papers 1425, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    7. Vladimir Vovk & Glenn Shafer, 2005. "Good randomized sequential probability forecasting is always possible," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(5), pages 747-763, November.
    8. Alvaro Sandroni & Rann Smorodinsky & Rakesh V. Vohra, 2003. "Calibration with Many Checking Rules," Mathematics of Operations Research, INFORMS, vol. 28(1), pages 141-153, February.
    9. Lehrer, Ehud, 2001. "Any Inspection Is Manipulable," Econometrica, Econometric Society, vol. 69(5), pages 1333-1347, September.
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    Cited by:

    1. Wojciech Olszewski & Alvaro Sandroni, 2008. "Manipulability of Future-Independent Tests," Econometrica, Econometric Society, vol. 76(6), pages 1437-1466, November.
    2. Yossi Feinberg & Nicolas Lambert, 2015. "Mostly calibrated," International Journal of Game Theory, Springer;Game Theory Society, vol. 44(1), pages 153-163, February.
    3. Olszewski, Wojciech, 2015. "Calibration and Expert Testing," Handbook of Game Theory with Economic Applications,, Elsevier.
    4. Wojciech Olszewski & Alvaro Sandroni, 2006. "Strategic Manipulation of Empirical Tests," Discussion Papers 1425, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    5. Dean Foster & Rakesh Vohra, 2011. "Calibration: Respice, Adspice, Prospice," Discussion Papers 1537, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    6. Itai Areili & Yakov Babichenko & Rann Smorodinsky, 2017. "Robust Forecast Aggregation," Papers 1710.02838, arXiv.org, revised Feb 2018.
    7. Kavaler, Itay & Smorodinsky, Rann, 2019. "On comparison of experts," Games and Economic Behavior, Elsevier, vol. 118(C), pages 94-109.
    8. Sylvain Chassang, 2013. "Calibrated Incentive Contracts," Econometrica, Econometric Society, vol. 81(5), pages 1935-1971, September.
    9. Colin, Stewart, 2011. "Nonmanipulable Bayesian testing," Journal of Economic Theory, Elsevier, vol. 146(5), pages 2029-2041, September.
    10. David Lagziel & Ehud Lehrer, 2021. "Transferable deposits as a screening mechanism," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 71(2), pages 483-504, March.
    11. Francisco Barreras & Álvaro José Riascos Villegas, 2016. "Screening multiple potentially false experts," Monografías 18207, Quantil.
    12. Alvaro Sandroni & Wojciech Olszewski, 2008. "Falsifiability," PIER Working Paper Archive 08-016, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
    13. Wojciech Olszewski & Alvaro Sandroni, 2009. "Strategic Manipulation of Empirical Tests," Mathematics of Operations Research, INFORMS, vol. 34(1), pages 57-70, February.
    14. Itay Kavaler & Rann Smorodinsky, 2019. "A Cardinal Comparison of Experts," Papers 1908.10649, arXiv.org, revised Feb 2020.

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