提出可随时检验条件均值函数的新型统计方法，支持实验中任意时刻下结论。
GAAVI: Global Asymptotic Anytime Valid Inference for the Conditional Mean Function
- 基于渐近无偏性设计，可在任意时间点进行有效推断。
- 在多种分布下保持名义误差率，且检验功效接近最优。
- 适合需持续监控的自适应实验与公平性审计场景。
条件均值函数（CMF）的推断在自适应实验、最优治疗分配和算法公平性审计中至关重要。本文提出一种新的渐近任意时间有效检验方法，用于检验CMF的全局零假设（如所有条件均值为零）及不同CMF间的差异，使实验者可在最小样本量后任意时间做出高置信度决策。在较弱条件下，该检验具有（i）渐近第一类错误控制，（ii）幂率为1，且（iii）相对于高斯位置检验展现出最优样本复杂度。通过反演检验，我们进一步构造了CMF及其对比的函数值渐近置信序列。合成与真实数据实验表明，该方法在多种分布下具有强检验功效，同时在连续监控下维持名义误差率。
原文摘要 · Abstract (English)
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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