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HOW TO AVOID THE ZERO-POWER TRAP IN TESTING FOR CORRELATION

Published online by Cambridge University Press:  01 March 2021

David Preinerstorfer*
Affiliation:
Université libre de Bruxelles
*
Address correspondence to David Preinerstorfer, European Center for Advanced Research in Economics and Statistics and Solvay Brussels School of Economics and Management, Université libre de Bruxelles, Avenue Franklin Roosevelt 50, 1050Bruxelles, Belgium; e-mail: david.preinerstorfer@ulb.be.

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 $1$ 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.

Type
ARTICLES
Copyright
© The Author(s), 2021. Published by Cambridge University Press

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Footnotes

I thank the Editor, Co-Editor, and two referees for helpful comments. Financial support by the Program of Concerted Research Actions (ARCs) of the Université libre de Bruxelles is gratefully acknowledged.

References

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