The multiply iterated LIL is derived as the minimax boundary of a sequential-detection game whose equalizer prior is the Jeffreys prior selected by the Erdős-Kolmogorov integral test, yielding a closed-form 3/2 coefficient correction.
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For bounded e-variables the GROW value equals the relative entropy of the weak-* joint information projection pair between arbitrary P and Q.
Finite-horizon optimal e-value designs for adaptive single-arm binary trials are constructed via dynamic programming and shown to have competitive operating characteristics with automatic futility indication.
The optimal wealth growth rate equals lim n→∞ of n^{-1} times inf KL(Q^n, P) over the bipolar of the n-fold null set, which is achievable and cannot be exceeded.
Introduces anytime-valid e-processes for first- and higher-order stochastic dominance that achieve power one and remain valid under continuous monitoring.
Power-one sequential tests exist for testing any weakly compact null set of distributions against its complement.
A distribution-free sequential test for return-to-baseline detection that aggregates a universal-inference discrepancy into a super-martingale and empirically calibrates it into an e-process with finite-sample bounds.
citing papers explorer
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The multiply iterated law of the iterated logarithm: game-theoretic foundations of sequential detection boundaries
The multiply iterated LIL is derived as the minimax boundary of a sequential-detection game whose equalizer prior is the Jeffreys prior selected by the Erdős-Kolmogorov integral test, yielding a closed-form 3/2 coefficient correction.
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Strong duality for the GROW criterion
For bounded e-variables the GROW value equals the relative entropy of the weak-* joint information projection pair between arbitrary P and Q.
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Adaptive clinical trials based on design-optimal e-values with automatic curtailment: An application to single-arm trials with binary data
Finite-horizon optimal e-value designs for adaptive single-arm binary trials are constructed via dynamic programming and shown to have competitive operating characteristics with automatic futility indication.
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The optimal betting wealth growth rate
The optimal wealth growth rate equals lim n→∞ of n^{-1} times inf KL(Q^n, P) over the bipolar of the n-fold null set, which is achievable and cannot be exceeded.
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Betting on Bets: Anytime-Valid Tests for Stochastic Dominance
Introduces anytime-valid e-processes for first- and higher-order stochastic dominance that achieve power one and remain valid under continuous monitoring.
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Power one sequential tests exist for weakly compact $\mathscr P$ against $\mathscr P^c$
Power-one sequential tests exist for testing any weakly compact null set of distributions against its complement.
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Return-to-Baseline Testing via Empirically Calibrated e-processes
A distribution-free sequential test for return-to-baseline detection that aggregates a universal-inference discrepancy into a super-martingale and empirically calibrates it into an e-process with finite-sample bounds.