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.

翻译：条件均值函数的推断在从自适应实验到最优治疗分配及算法公平性审计等任务中至关重要。本研究提出了一种新颖的渐近任意时间有效检验方法，用于检验条件均值函数的全局零假设（例如所有条件均值均为零）以及条件均值函数间的对比，使实验者能够在超过最小样本量后的任意实验时刻做出高置信度决策。我们给出了温和条件，在此条件下所提检验方法能够实现：（i）渐近第一类错误保证，（ii）功效为一，且与以往检验不同，（iii）相对于高斯位置检验具有最优样本复杂度。通过检验的反演，我们展示了如何为条件均值函数及其对比构建函数值渐近置信序列。在合成数据与真实数据上的实验表明，本方法在多种分布下均具有良好的功效，同时在连续监测下保持了名义错误率。