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How to avoid the zero-power trap in testing for correlation

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  • David Preinerstorfer

Abstract

In testing for correlation of the errors in regression models the power of tests can be very low for strongly correlated errors. This counterintuitive phenomenon has become known as the "zero-power trap". Despite a considerable amount of literature devoted to this problem, mainly focusing on its detection, a convincing solution has not yet been found. In this article we first discuss theoretical results concerning the occurrence of the zero-power trap phenomenon. Then, we suggest and compare three ways to avoid it. Given an initial test that suffers from the zero-power trap, the method we recommend for practice leads to a modified test whose power converges to one as the correlation gets very strong. Furthermore, the modified test has approximately the same power function as the initial test, and thus approximately preserves all of its optimality properties. We also provide some numerical illustrations in the context of testing for network generated correlation.

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  • David Preinerstorfer, 2018. "How to avoid the zero-power trap in testing for correlation," Papers 1812.10752, arXiv.org.
    • Handle: RePEc:arx:papers:1812.10752
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    References listed on IDEAS

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    1. Martellosio, Federico, 2010. "Power Properties Of Invariant Tests For Spatial Autocorrelation In Linear Regression," Econometric Theory, Cambridge University Press, vol. 26(1), pages 152-186, February.
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    3. Federico Martellosio, 2012. "Testing for Spatial Autocorrelation: The Regressors that Make the Power Disappear," Econometric Reviews, Taylor & Francis Journals, vol. 31(2), pages 215-240.
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    8. Preinerstorfer, David & Pötscher, Benedikt M., 2016. "On Size And Power Of Heteroskedasticity And Autocorrelation Robust Tests," Econometric Theory, Cambridge University Press, vol. 32(2), pages 261-358, April.
    9. Preinerstorfer, David & Pötscher, Benedikt M., 2017. "On The Power Of Invariant Tests For Hypotheses On A Covariance Matrix," Econometric Theory, Cambridge University Press, vol. 33(1), pages 1-68, February.
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