We prove a filtration-level conversion from uniform fixed-time testing to all-sample one-sided error control and uniform future-tail control. Given an adapted deterministic binary test whose worst-case fixed-time error tends to zero, the construction selects update times with prescribed summable error budgets and holds each selected decision until the next update. For every prescribed significance level, the construction yields a test that controls Type I error at every sample size; from each update time onward, the probability of any subsequent error is bounded uniformly over each hypothesis class by the remaining budget. Hence the test is uniformly consistent and eventually correct almost surely under both hypotheses. Applying the conversion to finite-alphabet coordinate processes proves the first implication in Ryabko's Conjecture 5.2.
We give a necessary and sufficient condition for the existence of power-one sequential tests in an i.i.d. composite testing problem. A level-\(\alpha\) test with power one against every alternative exists if and only if the alternatives are separated from the null by a countable family of finite-block events. We provid...
A deterministic target-transfer theorem is established for uniform, nonnested additive public cuts that bounds full-cut exploitability by regret on the delivered feedback and a public-debit term that couples prefix coverage discrepancy with motion along the realized strategy path.
We investigate composite binary hypothesis testing in the finite sample regime under asymmetric error constraints. Using R\'enyi divergences, we derive explicit achievability and converse bounds for the optimal Type II error. When the Type I error is constrained to decay exponentially with sample size, the bounds ident...
In safe hypothesis testing with test supermartingals, Ville's inequality provides anytime-valid type-I error guarantees for every significance level $\alpha\in(0,1]$, if one rejects the null hypothesis whenever the wealth process first exceeds $\frac{1}{\alpha}$. Due to an inherent asymmetry, the type-II error does not...
It is proved that testing is no more efficient than learning for halfspaces in the distribution-free sample-based model, and it is established that two-sided halfspace testers in this model have no advantage over one-sided testers.
Xi Chen, Renato Ferreira Pinto, Nathaniel Harms et al.· 0 citations
This paper proposes and studies a likelihood-ratio test of the null hypothesis that weak stochastic transitivity (WST) does not hold. This is the reverse of the formulation commonly used in the literature, where WST is set as the null hypothesis. We show that, even when the number of items grows with the number of comp...
Masaki Toyoda· 0 citations
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