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Good randomized sequential probability forecasting is always possible

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  • Vladimir Vovk
  • Glenn Shafer

Abstract

Summary. Building on the game theoretic framework for probability, we show that it is possible, using randomization, to make sequential probability forecasts that will pass any given battery of statistical tests. This result, an easy consequence of von Neumann's minimax theorem, simplifies and generalizes work by earlier researchers.

Suggested Citation

  • Vladimir Vovk & Glenn Shafer, 2005. "Good randomized sequential probability forecasting is always possible," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(5), pages 747-763, November.
    • Handle: RePEc:bla:jorssb:v:67:y:2005:i:5:p:747-763
    DOI: 10.1111/j.1467-9868.2005.00525.x
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    Cited by:

    1. Yossi Feinberg & Nicolas Lambert, 2015. "Mostly calibrated," International Journal of Game Theory, Springer;Game Theory Society, vol. 44(1), pages 153-163, February.
    2. Emilio Zanetti Chini, 2019. "Strategic judgment: its game-theoretic foundations,its econometric elicitation," Working Papers in Public Economics 190, University of Rome La Sapienza, Department of Economics and Law.
    3. Wojciech Olszewski & Alvaro Sandroni, 2006. "Strategic Manipulation of Empirical Tests," Discussion Papers 1425, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    4. Wojciech Olszewski & Alvaro Sandroni, 2008. "Manipulability of Future-Independent Tests," Econometrica, Econometric Society, vol. 76(6), pages 1437-1466, November.
    5. Dean Foster & Rakesh Vohra, 2011. "Calibration: Respice, Adspice, Prospice," Discussion Papers 1537, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    6. Chini, Emilio Zanetti, 2023. "Can we estimate macroforecasters’ mis-behavior?," Journal of Economic Dynamics and Control, Elsevier, vol. 149(C).
    7. Colin, Stewart, 2011. "Nonmanipulable Bayesian testing," Journal of Economic Theory, Elsevier, vol. 146(5), pages 2029-2041, September.
    8. Horikoshi, Yasunori & Takemura, Akimichi, 2008. "Implications of contrarian and one-sided strategies for the fair-coin game," Stochastic Processes and their Applications, Elsevier, vol. 118(11), pages 2125-2142, November.
    9. Roopesh Ranjan & Tilmann Gneiting, 2010. "Combining probability forecasts," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 72(1), pages 71-91, January.
    10. Wojciech Olszewski & Marcin Pęski, 2011. "The Principal-Agent Approach to Testing Experts," American Economic Journal: Microeconomics, American Economic Association, vol. 3(2), pages 89-113, May.
    11. Wojciech Olszewski & Alvaro Sandroni, 2009. "Strategic Manipulation of Empirical Tests," Mathematics of Operations Research, INFORMS, vol. 34(1), pages 57-70, February.
    12. Yossi Feinberg & Colin Stewart, 2008. "Testing Multiple Forecasters," Econometrica, Econometric Society, vol. 76(3), pages 561-582, May.
    13. Olszewski, Wojciech, 2015. "Calibration and Expert Testing," Handbook of Game Theory with Economic Applications,, Elsevier.
    14. Wojciech Olszewski & Alvaro Sandroni, 2011. "Falsifiability," American Economic Review, American Economic Association, vol. 101(2), pages 788-818, April.
    15. Alvaro Sandroni & Wojciech Olszewski, 2008. "Falsifiability," PIER Working Paper Archive 08-016, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.

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