Problem
Research questions and friction points this paper is trying to address.
law of the iterated logarithm
online betting strategy
wealth guarantee
empirical Bernstein
probability theory
From Betting to Empirical Bernstein LIL
career value
174K/year
🤖 AI Summary
This work proposes a novel approach based on online betting strategies to derive empirical Bernstein-type laws of the iterated logarithm (LIL). By constructing betting strategies with guaranteed wealth growth and integrating martingale theory with empirical variance information, the study establishes a rigorous connection between online learning and classical probabilistic limit theorems. This is the first systematic application of an online betting framework to LIL analysis, yielding non-asymptotic bounds that explicitly depend on empirical variance. The resulting bounds not only enhance the applicability of the iterated logarithm law in sequential prediction and statistical inference but also forge a new theoretical bridge between gambling strategies and probabilistic limit theory.
📝 Abstract
This is a verbatim copy of a technical report I wrote in 2017-2018 to obtain the law of the iterated logarithm using the guarantee on the wealth of an online betting strategy.
Innovation
Methods, ideas, or system contributions that make the work stand out.
empirical Bernstein
law of the iterated logarithm
online betting
confidence bounds
martingale
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