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Testing theories with learnable and predictive representations

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Author Info

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

Abstract

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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Bibliographic Info

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

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Web page: http://www.elsevier.com/locate/inca/622869

Related research

Keywords: Learning Expert testing;

References

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  1. Ehud Lehrer, 2003. "Approachability in infinite dimensional spaces," International Journal of Game Theory, Springer, vol. 31(2), pages 253-268.
  2. Sorin, Sylvain, 1999. "Merging, Reputation, and Repeated Games with Incomplete Information," Games and Economic Behavior, Elsevier, vol. 29(1-2), pages 274-308, October.
  3. Nabil I. Al-Najjar & Jonathan Weinstein, 2006. "Comparative Testing of Experts," Levine's Working Paper Archive 321307000000000590, David K. Levine.
  4. Matthew O. Jackson & Ehud Kalai & Rann Smorodinsky, 1998. "Bayesian Representation of Stochastic Processes under Learning: de Finetti Revisited," Discussion Papers 1228, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  5. Ehud Kalai, 1995. "Calibrated Forecasting and Merging," Discussion Papers 1144R, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  6. Alvaro Sandroni & Wojciech Olszewski, 2008. "Manipulability of Future-Independent Tests," PIER Working Paper Archive 08-014, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
  7. D. Foster & R. Vohra, 2010. "Asymptotic Calibration," Levine's Working Paper Archive 468, David K. Levine.
  8. Fudenberg, Drew & Levine, David, 1999. "An Easier Way to Calibrate," Scholarly Articles 3203773, Harvard University Department of Economics.
  9. Wojciech Olszewski & Alvaro Sandroni, 2006. "Strategic Manipulation of Empirical Tests," Discussion Papers 1425, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  10. Alvaro Sandroni, 2003. "The reproducible properties of correct forecasts," International Journal of Game Theory, Springer, vol. 32(1), pages 151-159, December.
  11. 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.
  12. Shmaya, Eran, 2008. "Many inspections are manipulable," Theoretical Economics, Econometric Society, vol. 3(3), September.
  13. Lance Fortnow & Rakesh V. Vohra, 2009. "The Complexity of Forecast Testing," Econometrica, Econometric Society, vol. 77(1), pages 93-105, 01.
  14. Lehrer, Ehud, 2001. "Any Inspection Is Manipulable," Econometrica, Econometric Society, vol. 69(5), pages 1333-47, September.
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Citations

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Cited by:
  1. Al-Najjar, Nabil & Sandroni, Alvaro, 2013. "A difficulty in the testing of strategic experts," Mathematical Social Sciences, Elsevier, vol. 65(1), pages 5-9.
  2. Dean Foster & Rakesh Vohra, 2011. "Calibration: Respice, Adspice, Prospice," Discussion Papers 1537, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  3. Wojciech Olszewski & Alvaro Sandroni, 2011. "Falsifiability," American Economic Review, American Economic Association, vol. 101(2), pages 788-818, April.
  4. Colin Stewart, 2009. "Nonmanipulable Bayesian Testing," Working Papers tecipa-360, University of Toronto, Department of Economics.
  5. Feinberg, Yossi & Lambert, Nicolas S., 2011. "Mostly Calibrated," Research Papers 2090, Stanford University, Graduate School of Business.
  6. Hu, Tai Wei & Shmaya, Eran, 2013. "Expressible inspections," Theoretical Economics, Econometric Society, vol. 8(2), May.

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