英文标题：
《Almost Similar Tests for Mediation Effects and other Hypotheses with
  Singularities》
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作者：
Kees Jan van Garderen, Noud van Giersbergen
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最新提交年份：
2020
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英文摘要：
  Testing for mediation effects is empirically important and theoretically interesting. It is important in psychology, medicine, economics, accountancy, and marketing for instance, generating over 90,000 citations to a single key paper in the field. It also leads to a statistically interesting and long-standing problem that this paper solves. The no-mediation hypothesis, expressed as $H_{0}:\\theta_{1}\\theta_{2}=0$, defines a manifold that is non-regular in the origin where rejection probabilities of standard tests are extremely low. We propose a general method for obtaining near similar tests using a flexible $g$-function to bound the critical region. We prove that no similar test exists for mediation, but using our new varying $g$-method obtain a test that is all but similar and easy to use in practice. We derive tight upper bounds to similar and nonsimilar power envelopes and derive an optimal test. We extend the test to higher dimensions and illustrate the results in a trade union sentiment application.
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中文摘要：
中介效应的测试在经验上很重要，在理论上也很有趣。例如，它在心理学、医学、经济学、会计学和市场营销等领域都很重要，在该领域的一篇关键论文中引用了90000多篇。这也导致了本文解决的一个统计上有趣且长期存在的问题。无中介假设表示为$H_{0}:\\theta_{1}\\theta_{2}=0$，它定义了一个流形，在标准测试的拒绝概率极低的情况下，流形在原点是不规则的。我们提出了一种获得近似相似测试的通用方法，使用灵活的$g$-函数来限制临界区域。我们证明不存在类似的中介测试，但使用我们新的可变$g$-方法可以获得一个几乎相似且易于在实践中使用的测试。我们推导了相似和非相似幂包络的紧上界，并给出了一个最优检验。我们将测试扩展到更高的维度，并在一个工会情绪应用程序中演示了测试结果。
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分类信息：

一级分类：Economics        经济学
二级分类：Econometrics        计量经济学
分类描述：Econometric Theory, Micro-Econometrics, Macro-Econometrics, Empirical Content of Economic Relations discovered via New Methods, Methodological Aspects of the Application of Statistical Inference to Economic Data.
计量经济学理论，微观计量经济学，宏观计量经济学，通过新方法发现的经济关系的实证内容，统计推论应用于经济数据的方法论方面。
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