Journal Article

Non-Bayesian Testing of a Stochastic Prediction

Eddie Dekel and Yossi Feinberg

in The Review of Economic Studies

Published on behalf of Review of Economic Studies Ltd

Volume 73, issue 4, pages 893-906
Published in print October 2006 | ISSN: 0034-6527
Published online October 2006 | e-ISSN: 1467-937X | DOI: http://dx.doi.org/10.1111/j.1467-937X.2006.00401.x
Non-Bayesian Testing of a Stochastic Prediction

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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.

Keywords: C12

Journal Article.  8921 words.  Illustrated.

Subjects: Econometric and Statistical Methods and Methodology: General

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