July  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), 2203-2217. 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

[1]

Chandan Pal, Somnath Pradhan. Zero-sum games for pure jump processes with risk-sensitive discounted cost criteria. Journal of Dynamics & Games, 2021  doi: 10.3934/jdg.2021020

[2]

Xiangxiang Huang, Xianping Guo, Jianping Peng. A probability criterion for zero-sum stochastic games. Journal of Dynamics & Games, 2017, 4 (4) : 369-383. doi: 10.3934/jdg.2017020

[3]

Marianne Akian, Stéphane Gaubert, Antoine Hochart. Ergodicity conditions for zero-sum games. Discrete & Continuous Dynamical Systems, 2015, 35 (9) : 3901-3931. doi: 10.3934/dcds.2015.35.3901

[4]

Sylvain Sorin, Guillaume Vigeral. Reversibility and oscillations in zero-sum discounted stochastic games. Journal of Dynamics & Games, 2015, 2 (1) : 103-115. doi: 10.3934/jdg.2015.2.103

[5]

Antoine Hochart. An accretive operator approach to ergodic zero-sum stochastic games. Journal of Dynamics & Games, 2019, 6 (1) : 27-51. doi: 10.3934/jdg.2019003

[6]

Alexander J. Zaslavski. Structure of approximate solutions of dynamic continuous time zero-sum games. Journal of Dynamics & Games, 2014, 1 (1) : 153-179. doi: 10.3934/jdg.2014.1.153

[7]

Qingmeng Wei, Zhiyong Yu. Time-inconsistent recursive zero-sum stochastic differential games. Mathematical Control & Related Fields, 2018, 8 (3&4) : 1051-1079. doi: 10.3934/mcrf.2018045

[8]

Beatris A. Escobedo-Trujillo. Discount-sensitive equilibria in zero-sum stochastic differential games. Journal of Dynamics & Games, 2016, 3 (1) : 25-50. doi: 10.3934/jdg.2016002

[9]

Fernando Luque-Vásquez, J. Adolfo Minjárez-Sosa. Average optimal strategies for zero-sum Markov games with poorly known payoff function on one side. Journal of Dynamics & Games, 2014, 1 (1) : 105-119. doi: 10.3934/jdg.2014.1.105

[10]

Alexander J. Zaslavski. Turnpike properties of approximate solutions of dynamic discrete time zero-sum games. Journal of Dynamics & Games, 2014, 1 (2) : 299-330. doi: 10.3934/jdg.2014.1.299

[11]

Salah Eddine Choutri, Boualem Djehiche, Hamidou Tembine. Optimal control and zero-sum games for Markov chains of mean-field type. Mathematical Control & Related Fields, 2019, 9 (3) : 571-605. doi: 10.3934/mcrf.2019026

[12]

Libin Mou, Jiongmin Yong. Two-person zero-sum linear quadratic stochastic differential games by a Hilbert space method. Journal of Industrial & Management Optimization, 2006, 2 (1) : 95-117. doi: 10.3934/jimo.2006.2.95

[13]

Fabien Gensbittel, Miquel Oliu-Barton, Xavier Venel. Existence of the uniform value in zero-sum repeated games with a more informed controller. Journal of Dynamics & Games, 2014, 1 (3) : 411-445. doi: 10.3934/jdg.2014.1.411

[14]

René Carmona, Kenza Hamidouche, Mathieu Laurière, Zongjun Tan. Linear-quadratic zero-sum mean-field type games: Optimality conditions and policy optimization. Journal of Dynamics & Games, 2021, 8 (4) : 403-443. doi: 10.3934/jdg.2021023

[15]

Zhi-Wei Sun. Unification of zero-sum problems, subset sums and covers of Z. Electronic Research Announcements, 2003, 9: 51-60.

[16]

Josef Hofbauer, Sylvain Sorin. Best response dynamics for continuous zero--sum games. Discrete & Continuous Dynamical Systems - B, 2006, 6 (1) : 215-224. doi: 10.3934/dcdsb.2006.6.215

[17]

Valery Y. Glizer, Oleg Kelis. Singular infinite horizon zero-sum linear-quadratic differential game: Saddle-point equilibrium sequence. Numerical Algebra, Control & Optimization, 2017, 7 (1) : 1-20. doi: 10.3934/naco.2017001

[18]

Dejian Chang, Zhen Wu. Stochastic maximum principle for non-zero sum differential games of FBSDEs with impulse controls and its application to finance. Journal of Industrial & Management Optimization, 2015, 11 (1) : 27-40. doi: 10.3934/jimo.2015.11.27

[19]

Jorge Clarke, Christian Olivera, Ciprian Tudor. The transport equation and zero quadratic variation processes. Discrete & Continuous Dynamical Systems - B, 2016, 21 (9) : 2991-3002. doi: 10.3934/dcdsb.2016083

[20]

Beatris Adriana Escobedo-Trujillo, José Daniel López-Barrientos. Nonzero-sum stochastic differential games with additive structure and average payoffs. Journal of Dynamics & Games, 2014, 1 (4) : 555-578. doi: 10.3934/jdg.2014.1.555

 Impact Factor: 

Metrics

  • PDF downloads (129)
  • HTML views (0)
  • Cited by (2)

Other articles
by authors

[Back to Top]