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July  2014, 1(3): 497-505. doi: 10.3934/jdg.2014.1.497

A prequential test for exchangeable theories

Alvaro Sandroni 1, and  Eran Shmaya 1,

1. 

Kellogg School of Management, Northwestern University, Evanston, Illinois 60208, United States, United States

Received  August 2012 Revised  March 2013 Published  July 2014

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.
Keywords: zero-sum games., merging, Calibration, expert testing, exchangeable processes.
Mathematics Subject Classification: Primary: 62A01; Secondary: 91A4.
Citation: Alvaro Sandroni, Eran Shmaya. A prequential test for exchangeable theories. Journal of Dynamics & Games, 2014, 1 (3) : 497-505. doi: 10.3934/jdg.2014.1.497
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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[5]

K. Fan, Minimax theorems, Proceedings of the National Academy of Sciences, 39 (1953), 42-47. doi: 10.1073/pnas.39.1.42.  Google Scholar

[6]

A. Kechris, Classical Descriptive Set Theory, Springer Verlag, 1995. doi: 10.1007/978-1-4612-4190-4.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[9]

D. Martin, The determinacy of Blackwell games, Journal of Symbolic Logic, 63 (1998), 1565-1581. doi: 10.2307/2586667.  Google Scholar

[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. Google Scholar

[11]

W. Olszewski and A. Sandroni, Manipulability of future-independent tests, Econometrica, 76 (2008), 1437-1466. doi: 10.3982/ECTA7428.  Google Scholar

[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.  Google Scholar

[13]

W. Olszewski and A. Sandroni, A nonmanipulable test, Annals of Statistics, 37 (2009), 1013-1039. doi: 10.1214/08-AOS597.  Google Scholar

[14]

A. Sandroni, The reproducible properties of correct forecasts, International Journal of Game Theory, 32 (2003), 151-159. doi: 10.1007/s001820300153.  Google Scholar

[15]

E. Shmaya, Many inspections are manipulable, Theoretical Economics, 3 (2008), 367-382. Google Scholar

[16]

S. Sorin, Merging, reputation, and repeated games with incomplete information, Games Econom. Behav., 29 (1999), 274-308. doi: 10.1006/game.1999.0722.  Google Scholar

[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.  Google Scholar

show all references

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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[5]

K. Fan, Minimax theorems, Proceedings of the National Academy of Sciences, 39 (1953), 42-47. doi: 10.1073/pnas.39.1.42.  Google Scholar

[6]

A. Kechris, Classical Descriptive Set Theory, Springer Verlag, 1995. doi: 10.1007/978-1-4612-4190-4.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[9]

D. Martin, The determinacy of Blackwell games, Journal of Symbolic Logic, 63 (1998), 1565-1581. doi: 10.2307/2586667.  Google Scholar

[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. Google Scholar

[11]

W. Olszewski and A. Sandroni, Manipulability of future-independent tests, Econometrica, 76 (2008), 1437-1466. doi: 10.3982/ECTA7428.  Google Scholar

[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.  Google Scholar

[13]

W. Olszewski and A. Sandroni, A nonmanipulable test, Annals of Statistics, 37 (2009), 1013-1039. doi: 10.1214/08-AOS597.  Google Scholar

[14]

A. Sandroni, The reproducible properties of correct forecasts, International Journal of Game Theory, 32 (2003), 151-159. doi: 10.1007/s001820300153.  Google Scholar

[15]

E. Shmaya, Many inspections are manipulable, Theoretical Economics, 3 (2008), 367-382. Google Scholar

[16]

S. Sorin, Merging, reputation, and repeated games with incomplete information, Games Econom. Behav., 29 (1999), 274-308. doi: 10.1006/game.1999.0722.  Google Scholar

[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.  Google Scholar

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