Structural assumptions are central to the causal inference literature. In practice, it is often crucial to assess their validity or to test implications that follow from them. In many settings, such tests can be framed as evaluating whether a function-valued parameter equals zero. In this paper, we propose a class of generalized projection tests based on series estimators for function-valued parameters. We establish conditions under which the proposed tests are valid and illustrate their applicability through examples from the data fusion and instrumental variables literature. Our approach accommodates flexible machine learning methods for estimating nuisance parameters. In contrast to many existing approaches, the limiting distribution of the proposed test statistics is straightforward to compute under the null hypothesis. We apply our method to test the equality of conditional COVID-19 risk across vaccine arms in the COVID-19 Variant Immunologic Landscape (COVAIL) trial.

翻译：结构假设是因果推断领域的核心要素。在实际应用中，评估其有效性或检验由其衍生的推论往往至关重要。此类检验常可转化为判断函数值参数是否等于零的问题。本文提出一类基于级数估计的广义投影检验方法，用于处理函数值参数的假设检验问题。我们建立了确保所提检验方法有效性的理论条件，并通过数据融合与工具变量领域的案例展示了其适用性。该方法支持使用灵活的机器学习技术进行干扰参数估计。与现有多数方法相比，所提检验统计量在原假设下的极限分布具有易于计算的特性。我们将该方法应用于COVID-19变异免疫图谱（COVAIL）临床试验中，检验不同疫苗组间条件性COVID-19感染风险的等价性假设。