Superconsistency of Tests in High Dimensions

Anders Kock and David Preinerstorfer

Papers from arXiv.org

Abstract: 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.

Date: 2021-06, Revised 2022-01
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Published in Econom. Theory 40 (2024) 688-704

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Persistent link: https://EconPapers.repec.org/RePEc:arx:papers:2106.03700

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