General sharpness, adaptive information control, and broader extensions of the minimax-quantile metaconverse

Determine general conditions under which the Neyman–Pearson metaconverse is attained, establish conditions under which a particular relaxation is sharp up to constants or exponents, develop systematic procedures for selecting the Sibson order or Young function from the structure of the success event and likelihood ratio, and extend the framework to interactive experiments, sequential procedures, and constrained decision rules.

Background

The paper develops a loss-adapted Neyman–Pearson metaconverse for minimax quantiles and derives relaxations based on f-informativity, Sibson information, Maximal Leakage, and Amemiya norms. Its applications show that the sharpness and usefulness of each relaxation depend on the recovery criterion and on the likelihood-ratio tail.

The conclusion explicitly identifies unresolved directions at three levels: characterizing when the master Neyman–Pearson converse or one of its relaxations is tight; choosing the Sibson order or Young function systematically rather than problem-by-problem; and extending the confidence-dependent converse framework beyond non-interactive experiments to sequential, interactive, and constrained decision settings.