arXiv 27 Dec 2018 · Mathematics — Statistics Theory · publishedEconometric Theory (2021) · 3 citations (OpenAlex)
arXiv:1812.10752 · PDF · DOI · OpenAlex · Extracted main text
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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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Preinerstorfer, D. and B. M. Pötscher (2017) On the power of invariant tests for hypotheses on a covariance matrix self | 1.000 | 35 | 8 | 100% |
| 2 | Krämer, W (1985) The power of the Durbin-Watson test for regressions without an intercept | 1.000 | 6 | 3 | 100% |
| 3 | Fan, J., Y. Liao, and J. Yao (2015) Power enhancement in high-dimensional cross-sectional tests | 0.928 | 4 | 3 | 100% |
| 4 | Krämer, W (2005) Finite sample power of Cliff-Ord-type tests for spatial disturbance correlation in linear regression | 0.928 | 4 | 3 | 100% |
| 5 | Martellosio, F (2010) Power properties of invariant tests for spatial autocorrelation in linear regression | 0.811 | 4 | 2 | 100% |
| 6 | Martellosio, F (2012) Testing for spatial autocorrelation: the regressors that make the power disappear | 0.737 | 3 | 2 | 100% |
| 7 | Kock, A. B. and D. Preinerstorfer (2017) Power in high-dimensional testing problems | 0.511 | 2 | 1 | 100% |
| 8 | Horn, R. A. and C. R. Johnson (1985) Matrix analysis | 0.405 | 1 | 1 | 100% |
| 9 | King, M. L. and G. H. Hillier (1985) Locally best invariant tests of the error covariance matrix of the linear regression model | 0.405 | 1 | 1 | 100% |
| 10 | Krämer, W. and H. Zeisel (1990) Finite sample power of linear regression autocorrelation tests | 0.405 | 1 | 1 | 100% |
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