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Almost Similar Tests for Mediation Effects and other Hypotheses with Singularities

Kees Jan van Garderen () and Noud van Giersbergen

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Abstract: 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.

Date: 2020-12
New Economics Papers: this item is included in nep-ecm
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