GAAVI: Global Asymptotic Anytime Valid Inference for the Conditional Mean Function

TL;DR

This paper introduces GAAVI, a novel asymptotic anytime-valid testing method for the conditional mean function, enabling high-confidence decisions during experiments with optimal sample complexity.

Contribution

The paper presents the first asymptotic anytime-valid test for the CMF that guarantees error control, high power, and optimal sample complexity, with applications to confidence sequences.

Findings

Achieves asymptotic type-I error guarantees.

Attains power one under mild conditions.

Maintains nominal error rate under continuous monitoring.

Abstract

Inference on the conditional mean function (CMF) is central to tasks from adaptive experimentation to optimal treatment assignment and algorithmic fairness auditing. In this work, we provide a novel asymptotic anytime-valid test for a CMF global null (e.g., that all conditional means are zero) and contrasts between CMFs, enabling experimenters to make high confidence decisions at any time during the experiment beyond a minimum sample size. We provide mild conditions under which our tests achieve (i) asymptotic type-I error guarantees, (i) power one, and, unlike past tests, (iii) optimal sample complexity relative to a Gaussian location testing. By inverting our tests, we show how to construct function-valued asymptotic confidence sequences for the CMF and contrasts thereof. Experiments on both synthetic and real-world data show our method is well-powered across various distributions while preserving the nominal error rate under continuous monitoring.