函数单调性的多重检验
Multiple testing of a function's monotonicity
- University of Missouri（密苏里大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文提出一种函数单调性的多重检验方法，可在多个点检验递增性，提供更细信息，并生成内外置信集，提高检验功效。
AI中文摘要：
我们不再仅仅对函数递增的全局零假设进行单一的“是”或“否”检验，而是提出了一种在多个点上检验函数递增性的多重检验程序。如果全局零假设被拒绝，多重检验能提供更多关于为何被拒绝的信息。如果全局零假设未被拒绝，多重检验则可以通过拒绝函数递减的零假设，为递增性提供更强的证据。我们的方法采用适用于广泛因果和描述性统计模型的高层次假设。通过反转所提出的控制族系错误率的多重检验程序，我们还为函数递增的点集生成了“内”和“外”置信集。在渐近概率下，内置信集包含于真实集合中，而外置信集包含真实集合。我们还通过逐步下降和两阶段程序提高了检验功效。模拟和实证例子说明了新方法，并提供了所有代码。
英文摘要：
Instead of having a single "yes" or "no" result from a test of the global null hypothesis that a function is increasing, we propose a multiple testing procedure of the function's increasingness at several points. If the global null is rejected, then multiple testing provides more information about why. If the global null is not rejected, then multiple testing can provide stronger evidence in favor of increasingness, by rejecting null hypotheses that the function is decreasing. Our approach uses high-level assumptions that apply to a broad class of causal and descriptive statistical models. By inverting the proposed multiple testing procedure that controls the familywise error rate, we also generate "inner" and "outer" confidence sets for the set of points at which the function is increasing. With high asymptotic probability, the inner confidence set is contained within the true set, whereas the outer confidence set contains the true set. We also improve power with stepdown and two-stage procedures. Simulation and empirical examples illustrate the new methodology, and all code is provided.
