Game-theoretic statistics and safe anytime-valid inference

TL;DR

This paper introduces safe anytime-valid inference (SAVI), a framework using game-theoretic concepts and test martingales to provide valid statistical measures at any stopping time, suitable for continuous data monitoring.

Contribution

It presents recent advances in applying SAVI to testing composite hypotheses and estimating functionals in nonparametric contexts, emphasizing its game-theoretic foundation.

Findings

SAVI ensures valid inference at arbitrary stopping times.

Recent methods improve testing composite hypotheses.

Estimation of functionals in nonparametric settings is now feasible with SAVI.

Abstract

Safe anytime-valid inference (SAVI) provides measures of statistical evidence and certainty -- e-processes for testing and confidence sequences for estimation -- that remain valid at all stopping times, accommodating continuous monitoring and analysis of accumulating data and optional stopping or continuation for any reason. These measures crucially rely on test martingales, which are nonnegative martingales starting at one. Since a test martingale is the wealth process of a player in a betting game, SAVI centrally employs game-theoretic intuition, language and mathematics. We summarize the SAVI goals and philosophy, and report recent advances in testing composite hypotheses and estimating functionals in nonparametric settings.