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

A prequential test for exchangeable theories

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.
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. 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. 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. doi: 10.1111/j.1467-937X.2006.00401.x.

[4]

A. P. Dawid, Statistical theory: The prequential approach,, Journal of the Royal Statistical Society, 147 (1984), 278. doi: 10.2307/2981683.

[5]

K. Fan, Minimax theorems,, Proceedings of the National Academy of Sciences, 39 (1953), 42. 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. 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. doi: 10.1006/game.1998.0608.

[9]

D. Martin, The determinacy of Blackwell games,, Journal of Symbolic Logic, 63 (1998), 1565. 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), (2014).

[11]

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

[12]

W. Olszewski and A. Sandroni, Strategic manipulation of empirical tests,, Mathematics of Operations Research, 34 (2009), 57. doi: 10.1287/moor.1080.0347.

[13]

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

[14]

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

[15]

E. Shmaya, Many inspections are manipulable,, Theoretical Economics, 3 (2008), 367.

[16]

S. Sorin, Merging, reputation, and repeated games with incomplete information,, Games Econom. Behav., 29 (1999), 274. 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, 67 (2005), 747. doi: 10.1111/j.1467-9868.2005.00525.x.

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. 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. 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. doi: 10.1111/j.1467-937X.2006.00401.x.

[4]

A. P. Dawid, Statistical theory: The prequential approach,, Journal of the Royal Statistical Society, 147 (1984), 278. doi: 10.2307/2981683.

[5]

K. Fan, Minimax theorems,, Proceedings of the National Academy of Sciences, 39 (1953), 42. 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. 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. doi: 10.1006/game.1998.0608.

[9]

D. Martin, The determinacy of Blackwell games,, Journal of Symbolic Logic, 63 (1998), 1565. 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), (2014).

[11]

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

[12]

W. Olszewski and A. Sandroni, Strategic manipulation of empirical tests,, Mathematics of Operations Research, 34 (2009), 57. doi: 10.1287/moor.1080.0347.

[13]

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

[14]

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

[15]

E. Shmaya, Many inspections are manipulable,, Theoretical Economics, 3 (2008), 367.

[16]

S. Sorin, Merging, reputation, and repeated games with incomplete information,, Games Econom. Behav., 29 (1999), 274. 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, 67 (2005), 747. doi: 10.1111/j.1467-9868.2005.00525.x.

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