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Testing theories with learnable and predictive representations

  • Al-Najjar, Nabil I.
  • Sandroni, Alvaro
  • Smorodinsky, Rann
  • Weinstein, Jonathan

We study the problem of testing an expert whose theory has a learnable and predictive parametric representation, as do standard processes used in statistics. We design a test in which the expert is required to submit a date T by which he will have learned enough to deliver a sharp, testable prediction about future frequencies. We show that this test passes an expert who knows the data-generating process and cannot be manipulated by a uninformed one. Such a test is not possible if the theory is unrestricted.

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Article provided by Elsevier in its journal Journal of Economic Theory.

Volume (Year): 145 (2010)
Issue (Month): 6 (November)
Pages: 2203-2217

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Handle: RePEc:eee:jetheo:v:145:y:2010:i:6:p:2203-2217
Contact details of provider: Web page: http://www.elsevier.com/locate/inca/622869

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  1. Sorin, Sylvain, 1999. "Merging, Reputation, and Repeated Games with Incomplete Information," Games and Economic Behavior, Elsevier, vol. 29(1-2), pages 274-308, October.
  2. Ehud Kalai & Ehud Lehrer, 1992. "Weak and Strong Merging of Opinions," Discussion Papers 983, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  3. Wojciech Olszewski & Alvaro Sandroni, 2008. "Manipulability of Future-Independent Tests," Econometrica, Econometric Society, vol. 76(6), pages 1437-1466, November.
  4. Nabil I. Al-Najjar & Jonathan Weinstein, 2006. "Comparative Testing of Experts," Levine's Working Paper Archive 321307000000000590, David K. Levine.
  5. Matthew O. Jackson & Ehud Kalai & Rann Smorodinsky, 1999. "Bayesian Representation of Stochastic Processes under Learning: de Finetti Revisited," Econometrica, Econometric Society, vol. 67(4), pages 875-894, July.
  6. Ehud Kalai & Ehud Lehrer & Rann Smorodinsky, 2010. "Calibrated Forecasting and Merging," Levine's Working Paper Archive 584, David K. Levine.
  7. Fudenberg, Drew & Levine, David K., 1999. "An Easier Way to Calibrate," Games and Economic Behavior, Elsevier, vol. 29(1-2), pages 131-137, October.
  8. Lehrer, Ehud, 2001. "Any Inspection Is Manipulable," Econometrica, Econometric Society, vol. 69(5), pages 1333-47, September.
  9. D. Foster & R. Vohra, 2010. "Asymptotic Calibration," Levine's Working Paper Archive 468, David K. Levine.
  10. Wojciech Olszewski & Alvaro Sandroni, 2006. "Strategic Manipulation of Empirical Tests," Discussion Papers 1425, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  11. Alvaro Sandroni, 2003. "The reproducible properties of correct forecasts," International Journal of Game Theory, Springer, vol. 32(1), pages 151-159, December.
  12. Lance Fortnow & Rakesh V. Vohra, 2009. "The Complexity of Forecast Testing," Econometrica, Econometric Society, vol. 77(1), pages 93-105, 01.
  13. Ehud Lehrer, 2003. "Approachability in infinite dimensional spaces," International Journal of Game Theory, Springer, vol. 31(2), pages 253-268.
  14. Shmaya, Eran, 2008. "Many inspections are manipulable," Theoretical Economics, Econometric Society, vol. 3(3), September.
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