Exponential inequalities and the law of the iterated logarithm in the unbounded forecasting game

@article{Takazawa2012ExponentialIA,
  title={Exponential inequalities and the law of the iterated logarithm in the unbounded forecasting game},
  author={Shin-ichiro Takazawa},
  journal={Annals of the Institute of Statistical Mathematics},
  year={2012},
  volume={64},
  pages={615-632}
}
We study the law of the iterated logarithm in the framework of game-theoretic probability of Shafer and Vovk. We investigate hedges under which a game-theoretic version of the upper bound of the law of the iterated logarithm holds without any condition on Reality’s moves in the unbounded forecasting game. We prove that in the unbounded forecasting game with an exponential hedge, Skeptic can force the upper bound of the law of the iterated logarithm without conditions on Reality’s moves. We give… CONTINUE READING
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