On a simple strategy weakly forcing the strong law of large numbers in the bounded forecasting game

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dc.creatorKumon, Masayuki
dc.creatorTakemura, Akimichi
dc.date2005-08-11
dc.date2005-11-10
dc.date.accessioned2026-07-07T12:34:37Z
dc.date.available2026-07-07T12:34:37Z
dc.descriptionIn the framework of the game-theoretic probability of Shafer and Vovk (2001) it is of basic importance to construct an explicit strategy weakly forcing the strong law of large numbers (SLLN) in the bounded forecasting game. We present a simple finite-memory strategy based on the past average of Reality's moves, which weakly forces the strong law of large numbers with the convergence rate of $O(\sqrt{\log n/n})$. Our proof is very simple compared to a corresponding measure-theoretic result of Azuma (1967) on bounded martingale differences and this illustrates effectiveness of game-theoretic approach. We also discuss one-sided protocols and extension of results to linear protocols in general dimension.
dc.description14 pages
dc.identifierhttps://arxiv.org/abs/math/0508190
dc.identifierhttp://arxiv.org/abs/math/0508190
dc.identifierAnnals of the Institute of Statistical Mathematics, Vol.60, No.4, 801-812. (2008)
dc.identifierdoi:10.1007/s10463-007-0125-5
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/217500
dc.subjectProbability
dc.subjectStatistics Theory
dc.subject60A10
dc.titleOn a simple strategy weakly forcing the strong law of large numbers in the bounded forecasting game
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