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文献的核心。在实践中，评估其有效性或检验由其衍生的推论通常至关重要。在许多场景下，此类检验可被构建为评估一个函数值参数是否等于零的问题。本文提出了一类基于级数估计器的函数值参数广义投影检验方法。我们建立了所提检验方法有效的条件，并通过数据融合和工具变量文献中的实例说明了其适用性。我们的方法支持使用灵活的机器学习方法来估计干扰参数。与许多现有方法相比，所提检验统计量在零假设下的极限分布易于计算。我们将该方法应用于COVID-19变异免疫学景观（COVAIL）试验中，以检验不同疫苗组间条件性COVID-19风险的相等性。