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Non-Bayesian Testing of a Stochastic Prediction

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Author Info
EDDIE DEKEL
YOSSI FEINBERG

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Abstract

We propose a method to test a prediction of the distribution of a stochastic process. In a non-Bayesian, non-parametric setting, a predicted distribution is tested using a realization of the stochastic process. A test associates a set of realizations for each predicted distribution, on which the prediction passes, so that if there are no type I errors, a prediction assigns probability 1 to its test set. Nevertheless, these test sets can be "small", in the sense that "most" distributions assign it probability 0, and hence there are "few" type II errors. It is also shown that there exists such a test that cannot be manipulated, in the sense that an uninformed predictor, who is pretending to know the true distribution, is guaranteed to fail on an uncountable number of realizations, no matter what randomized prediction he employs. The notion of a small set we use is category I, described in more detail in the paper. Copyright 2006 The Review of Economic Studies Limited.

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File URL: http://www.blackwell-synergy.com/doi/abs/10.1111/j.1467-937X.2006.00401.x
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Publisher Info
Article provided by Blackwell Publishing in its journal Review of Economic Studies.

Volume (Year): 73 (2006)
Issue (Month): 4 (October)
Pages: 893-906
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Handle: RePEc:bla:restud:v:73:y:2006:i:4:p:893-906

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  1. Sandroni, Alvaro & Smorodinsky, Rann, 2004. "Belief-based equilibrium," Games and Economic Behavior, Elsevier, vol. 47(1), pages 157-171, April. [Downloadable!] (restricted)
  2. Fudenberg, Drew & Levine, David K., 1999. "Conditional Universal Consistency," Games and Economic Behavior, Elsevier, vol. 29(1-2), pages 104-130, October. [Downloadable!] (restricted)
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  3. Ehud Kalai, 1995. "Calibrated Forecasting and Merging," Discussion Papers 1144, Northwestern University, Center for Mathematical Studies in Economics and Management Science. [Downloadable!]
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  4. Fudenberg, Drew & Levine, David K., 1995. "Consistency and cautious fictitious play," Journal of Economic Dynamics and Control, Elsevier, vol. 19(5-7), pages 1065-1089. [Downloadable!] (restricted)
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  5. Hart, Sergiu & Mas-Colell, Andreu, 2001. "A General Class of Adaptive Strategies," Journal of Economic Theory, Elsevier, vol. 98(1), pages 26-54, May. [Downloadable!] (restricted)
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  6. Foster, Dean P. & Vohra, Rakesh V., 1997. "Calibrated Learning and Correlated Equilibrium," Games and Economic Behavior, Elsevier, vol. 21(1-2), pages 40-55, October. [Downloadable!] (restricted)
  7. Lehrer, Ehud, 2001. "Any Inspection Is Manipulable," Econometrica, Econometric Society, vol. 69(5), pages 1333-47, September.
  8. Sergiu Hart & Andreu Mas-Colell, 2000. "A Simple Adaptive Procedure Leading to Correlated Equilibrium," Econometrica, Econometric Society, vol. 68(5), pages 1127-1150, September.
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Cited by:
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  1. 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. [Downloadable!]
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  2. Alvaro Sandroni & Wojciech Olszewski, 2008. "Falsifiability," PIER Working Paper Archive 08-016, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania. [Downloadable!]
  3. Echenique, Federico & Shmaya, Eran, 2007. "You won’t harm me if you fool me," Working Papers 1281, California Institute of Technology, Division of the Humanities and Social Sciences. [Downloadable!]
  4. Colin Stewart, 2009. "Nonmanipulable Bayesian Testing," Working Papers tecipa-360, University of Toronto, Department of Economics. [Downloadable!]
  5. Alvaro Sandroni & Wojciech Olszewski, 2008. "Strategic Manipulation of Empirical Tests," PIER Working Paper Archive 08-015, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania. [Downloadable!]
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  6. Feinberg, Yossi & Stewart, Colin, 2007. "Testing Multiple Forecasters," Research Papers 1957, Stanford University, Graduate School of Business. [Downloadable!]
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