Test Martingale
A stochastic process constructed by multiplying e-values sequentially, whose expected value under the null hypothesis does not exceed its initial value. It is the core mathematical tool underpinning anytime-valid statistical inference.
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Multiplying conditional e-values sequentially yields a test martingale, and taking the inverse of the test martingale over the parameter space produces a confidence sequence for the parameter.
The key property of e-values is that if the null hypothesis H₀ is true, the expected value of the e-value does not exceed 1, which allows e-values to be safely multiplied sequentially to form a test martingale.
Anytime-valid methods based on test martingales are designed to avoid the type I error inflation caused by traditional p-values in scenarios of multiple testing or continuous monitoring.
All Facts (3)
Multiplying conditional e-values sequentially yields a test martingale, and taking the inverse of the test martingale over the parameter space produces a confidence sequence for the parameter.
50%UnverifiedThe key property of e-values is that if the null hypothesis H₀ is true, the expected value of the e-value does not exceed 1, which allows e-values to be safely multiplied sequentially to form a test martingale.
50%UnverifiedAnytime-valid methods based on test martingales are designed to avoid the type I error inflation caused by traditional p-values in scenarios of multiple testing or continuous monitoring.
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