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 there are no type I errors, a prediction assigns probability 1 to its test set. Nevertheless, these sets are 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.
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Paper provided by Northwestern University, Center for Mathematical Studies in Economics and Management Science in its series Discussion Papers with number
1418.
Length: Date of creation: Jan 2006 Date of revision: Handle: RePEc:nwu:cmsems:1418
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References listed on IDEAS Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
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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Cited by: (explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)
Alvaro Sandroni & Wojciech Olszewski, 2008.
"Falsifiability,"
PIER Working Paper Archive
08-016, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
[Downloadable!]
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!]