Statistical inference of directed relations given some unspecified interventions (i.e., the intervention targets are unknown) is challenging. In this article, we test hypothesized directed relations with unspecified interventions. First, we derive conditions to yield an identifiable model. Unlike classical inference, testing directed relations requires identifying the ancestors and relevant interventions of hypothesis-specific primary variables. To this end, we propose a peeling algorithm based on nodewise regressions to establish a topological order of primary variables. Moreover, we prove that the peeling algorithm yields a consistent estimator in low-order polynomial time. Second, we propose a likelihood ratio test integrated with a data perturbation scheme to account for the uncertainty of identifying ancestors and interventions. Also, we show that the distribution of a data perturbation test statistic converges to the target distribution. Numerical examples demonstrate the utility and effectiveness of the proposed methods, including an application to infer gene regulatory networks. The R implementation is available at https://github.com/chunlinli/intdag.

翻译：根据一些未说明的干预措施(即,干预目标未知),直接关系的统计推论具有挑战性。在本条中,我们测试与未说明的干预措施的假设性直接关系。首先,我们提出产生可识别模型的条件。与传统的推论不同,测试直接关系要求确定祖先和具体假设主要变量的相关干预措施。为此,我们提议基于无偏向回归的剥离算法,以建立主要变量的地貌顺序。此外,我们证明剥离算法在低顺序多义时产生了一致的测算器。第二,我们提议与数据渗透性计划相结合的可能性比率测试,以说明识别祖先和干预措施的不确定性。此外,我们还表明数据扰动测试统计数据的分布与目标分布一致。数字实例表明拟议方法的效用和有效性,包括用于推导基因管理网络的应用。R的落实情况可在https://github.com/chunlinli/intdag查阅。</s>