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

• URL: http://arxiv.org/abs/2602.08096v1
• Date: Sun, 08 Feb 2026 19:34:18 GMT
• Title: GAAVI: Global Asymptotic Anytime Valid Inference for the Conditional Mean Function
• Authors: Brian M Cho, Raaz Dwivedi, Nathan Kallus,
• Abstract summary: We provide a novel anytime-valid test for a CMF global null.<n>We show how to construct function-valued confidence for the CMF and contrasts thereof.<n>Our method is well-powered across various distributions while preserving the nominal error rate under continuous monitoring.
• Score: 40.13687327412775
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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