Sharper multiplicity control and finite-sample estimator theory

Develop sharper-than-union-bound multiplicity control for the restarted e-detector, including mixture e-values, and establish finite-sample theory for the underlying estimator used by the conditional Jensen–Shannon discrepancy framework.

Background

The paper establishes validity for bounded-memory recency through a restarted e-detector whose restart instances receive an alpha-spending schedule. This construction controls multiplicity by a union bound over all restart instances, but the authors identify sharper-than-union-bound methods, such as mixture e-values, as unresolved. The paper also relies on an underlying estimator for the conditional Jensen–Shannon discrepancy and explicitly notes that its finite-sample theory remains to be developed in the companion theoretical work. These issues concern strengthening the statistical foundations of the deployed decision layer beyond the guarantees proved in the paper.