We present a general nonparametric approach for testing whether a statistical parameter defined through conditional distributions is constant across the conditioning variables. Such hypotheses arise naturally in problems such as assessing treatment effect heterogeneity, conditional associational effects, and conditional mean dependence. Our framework studies function-valued parameters obtained by evaluating a smooth statistical functional on conditional probability distributions. We establish an explicit connection between our test and procedures based on studying the norm of the function-valued parameter. Unlike many existing norm-based tests, which exhibit poor asymptotic behavior under the null, the proposed test statistic admits a tractable limiting null distribution. We illustrate the applicability of the proposed test through several examples, assess its operating characteristics in simulation studies, and apply it to data from a breast cancer trial to identify predictive biomarkers for response to adjuvant chemotherapy.

翻译：我们提出了一种通用非参数方法，用于检验通过条件分布定义的统计参数是否在条件变量间保持恒定。此类假设自然出现在以下问题中：评估治疗效应异质性、条件关联效应以及条件均值依赖性。我们的框架通过评估条件概率分布上的平滑统计泛函，研究函数值参数。我们建立了该检验方法与基于函数值参数范数研究的过程之间的显式联系。与许多在零假设下渐近行为较差的现有范数基检验不同，所提出的检验统计量具有可处理的零极限分布。我们通过若干实例说明该检验的适用性，在模拟研究中评估其运行特性，并将其应用于一项乳腺癌试验数据，以识别对辅助化疗反应的预测性生物标志物。