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Log-optimal anytime-valid E-values
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DOI：10.1016/j.ijar.2021.09.010.png)
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Abstract
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We consider the problem of measuring statistical evidence against a composite null hypothesis. We base our approach on the concept of an E-value, which measures evidence by the multiplication factor achieved by engaging in bets that are fair under the null. We adopt the log-optimality criterion for choosing among all possible E-values, which was considered earlier for a fixed sample size. We extend these ideas to sequential testing under optional stopping, by revisiting anytime-valid E-values. Our main contribution is the formulation of a sequential log-optimality criterion. We study its properties, and work out examples analytically and computationally. (C) 2021 The Author(s). Published by Elsevier Inc.
Keywords:
E-value
Anytime-valid E-value
Hypothesis testing
Test martingales
Betting score
Implied target
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