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Mostly calibrated

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  • Yossi Feinberg

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  • Nicolas Lambert

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Abstract

Prequential testing of a forecaster is known to be manipulable if the test must pass an informed forecaster for all possible true distributions. Stewart (J Econ Theory 146(5):2029–2041, 2011 ) provides a non-manipulable prequential likelihood test that only fails an informed forecaster on a small, category I, set of distributions. We present a prequential test based on calibration that also fails the informed forecaster on at most a category I set of true distributions and is non-manipulable. Our construction sheds light on the relationship between likelihood and calibration with respect to the distributions they reject. Copyright Springer-Verlag Berlin Heidelberg 2015

Suggested Citation

  • Yossi Feinberg & Nicolas Lambert, 2015. "Mostly calibrated," International Journal of Game Theory, Springer;Game Theory Society, vol. 44(1), pages 153-163, February.
  • Handle: RePEc:spr:jogath:v:44:y:2015:i:1:p:153-163
    DOI: 10.1007/s00182-014-0423-0
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    File URL: http://hdl.handle.net/10.1007/s00182-014-0423-0
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    References listed on IDEAS

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    1. Nabil I. Al-Najjar & Jonathan Weinstein, 2008. "Comparative Testing of Experts," Econometrica, Econometric Society, vol. 76(3), pages 541-559, May.
    2. Wojciech Olszewski & Alvaro Sandroni, 2008. "Manipulability of Future-Independent Tests," Econometrica, Econometric Society, vol. 76(6), pages 1437-1466, November.
    3. Fudenberg, Drew & Levine, David K., 1999. "An Easier Way to Calibrate," Games and Economic Behavior, Elsevier, vol. 29(1-2), pages 131-137, 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. 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.
    6. Kalai, Ehud & Lehrer, Ehud & Smorodinsky, Rann, 1999. "Calibrated Forecasting and Merging," Games and Economic Behavior, Elsevier, vol. 29(1-2), pages 151-169, October.
    7. Al-Najjar, Nabil I. & Sandroni, Alvaro & Smorodinsky, Rann & Weinstein, Jonathan, 2010. "Testing theories with learnable and predictive representations," Journal of Economic Theory, Elsevier, vol. 145(6), pages 2203-2217, November.
    8. Eddie Dekel & Yossi Feinberg, 2006. "Non-Bayesian Testing of a Stochastic Prediction," Review of Economic Studies, Oxford University Press, vol. 73(4), pages 893-906.
    9. Colin, Stewart, 2011. "Nonmanipulable Bayesian testing," Journal of Economic Theory, Elsevier, vol. 146(5), pages 2029-2041, September.
    10. Shmaya, Eran, 2008. "Many inspections are manipulable," Theoretical Economics, Econometric Society, vol. 3(3), September.
    11. Yossi Feinberg & Colin Stewart, 2008. "Testing Multiple Forecasters," Econometrica, Econometric Society, vol. 76(3), pages 561-582, May.
    12. Lehrer, Ehud, 2001. "Any Inspection Is Manipulable," Econometrica, Econometric Society, vol. 69(5), pages 1333-1347, September.
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    Keywords

    Testing forecasters; Calibration test;

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