Anders Bredahl Kock, David Preinerstorfer
arXiv 7 Jun 2021 · Mathematics — Statistics Theory · publishedEconometric Theory (2022)
arXiv:2106.03700 · PDF · DOI · OpenAlex · Extracted main text
To assess whether there is some signal in a big database, aggregate tests for the global null hypothesis of no effect are routinely applied in practice before more specialized analysis is carried out. Although a plethora of aggregate tests is available, each test has its strengths but also its blind spots. In a Gaussian sequence model, we study whether it is possible to obtain a test with substantially better consistency properties than the likelihood ratio (i.e., Euclidean norm based) test. We establish an impossibility result, showing that in the high-dimensional framework we consider, the set of alternatives for which a test may improve upon the likelihood ratio test -- that is, its superconsistency points -- is always asymptotically negligible in a relative volume sense.
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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.
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|---|---|---|---|---|---|
| 1 | Kock, A. B. and Preinerstorfer, D (2021) Consistency of $ p $-norm based tests in high dimensions: characterization, monotonicity, domination self | 1.000 | 6 | 4 | 100% |
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