A prequential test for exchangeable theories

Alvaro Sandroni; Eran Shmaya

doi:10.3934/jdg.2014.1.497

Article Contents

2014, Volume 1, Issue 3: 497-505. Doi: 10.3934/jdg.2014.1.497

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A prequential test for exchangeable theories

Alvaro Sandroni^1, and
Eran Shmaya^1,

1.
Kellogg School of Management, Northwestern University, Evanston, Illinois 60208

Received: July 31, 2012

Revised: February 28, 2013

Published: June 2014

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Abstract

We construct a prequential test of probabilistic forecasts that does not reject correct forecasts when the data-generating processes is exchangeable and is not manipulable by a false forecaster.

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Mathematics Subject Classification: Primary: 62A01; Secondary: 91A40.

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References

[1]	N. Al-Najjar, R. Smorodinsky, A. Sandroni and J. Weinstein, Testing theories with learnable and predictive representations, Journal of Economic Theory, 145 (2010), 2203-2217.doi: 10.1016/j.jet.2010.07.003.
[2]	D. Blackwell and L. Dubins, Merging of opinions with increasing information, Annals of Mathematical Statistics, 33 (1962), 882-886.doi: 10.1214/aoms/1177704456.
[3]	E. Dekel and Y. Feinberg, Non-Bayesian testing of a stochastic prediction, Review of Economic Studies, 73 (2006), 893-906.doi: 10.1111/j.1467-937X.2006.00401.x.
[4]	A. P. Dawid, Statistical theory: The prequential approach, Journal of the Royal Statistical Society, Series A, 147 (1984), 278-292.doi: 10.2307/2981683.
[5]	K. Fan, Minimax theorems, Proceedings of the National Academy of Sciences, 39 (1953), 42-47.doi: 10.1073/pnas.39.1.42.
[6]	A. Kechris, Classical Descriptive Set Theory, Springer Verlag, 1995.doi: 10.1007/978-1-4612-4190-4.
[7]	E. Kalai and E. Lehrer, Weak and strong merging of opinions, J. Math. Econom., 23 (1994), 73-86.doi: 10.1016/0304-4068(94)90037-X.
[8]	E. Kalai, E. Lehrer and R. Smorodinsky, Calibrated forecasting and merging, Games Econom. Behav., 29 (1999), 151-169.doi: 10.1006/game.1998.0608.
[9]	D. Martin, The determinacy of Blackwell games, Journal of Symbolic Logic, 63 (1998), 1565-1581.doi: 10.2307/2586667.
[10]	W. Olszewski, Calibration and Expert Testing, in Handbook of Game Theory with Economic Applications (eds. H. Petyon Young and Shmuel Zamir), Vol. IV, North Holland, 2014.
[11]	W. Olszewski and A. Sandroni, Manipulability of future-independent tests, Econometrica, 76 (2008), 1437-1466.doi: 10.3982/ECTA7428.
[12]	W. Olszewski and A. Sandroni, Strategic manipulation of empirical tests, Mathematics of Operations Research, 34 (2009), 57-70.doi: 10.1287/moor.1080.0347.
[13]	W. Olszewski and A. Sandroni, A nonmanipulable test, Annals of Statistics, 37 (2009), 1013-1039.doi: 10.1214/08-AOS597.
[14]	A. Sandroni, The reproducible properties of correct forecasts, International Journal of Game Theory, 32 (2003), 151-159.doi: 10.1007/s001820300153.
[15]	E. Shmaya, Many inspections are manipulable, Theoretical Economics, 3 (2008), 367-382.
[16]	S. Sorin, Merging, reputation, and repeated games with incomplete information, Games Econom. Behav., 29 (1999), 274-308.doi: 10.1006/game.1999.0722.
[17]	V. Vovk and G. Shafer, Good randomized sequential probability forecasting is always possible, Journal of the Royal Statistical Society, Series B, 67 (2005), 747-763.doi: 10.1111/j.1467-9868.2005.00525.x.