Superconsistency of tests in high dimensions

Journal article

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 (LR; 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 LR test (i.e., its superconsistency points) is always asymptotically negligible in a relative volume sense.

Authors: Kock, A; Preinerstorfer, D

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: Cambridge University Press
• Journal: Econometric Theory
• Volume: 40
• Issue: 3
• Pages: 688-704
• Publication date: 2022-10-28
• Acceptance date: 2022-08-16
• DOI: 10.1017/S0266466622000482
• EISSN: 1469-4360
• ISSN: 0266-4666
• Language: English
• Keywords: power enhancement; high-dimensional testing problems; big data; power; superconsistency; concentration of measure