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SUPERCONSISTENCY OF TESTS IN HIGH DIMENSIONS

Published online by Cambridge University Press:  28 October 2022

Anders Bredahl Kock  and
David Preinerstorfer
Anders Bredahl Kock*
Affiliation:
University of Oxford
David Preinerstorfer
Affiliation:
University of St. Gallen
*
Address correspondence to Anders Bredahl Kock, University of Oxford, 10 Manor Road, Oxford OX1 3UQ, UK; e-mail: [email protected].
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Abstract

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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.

Type
MISCELLANEA
Information
Econometric Theory , Volume 40 , Issue 3 , June 2024 , pp. 688 - 704
Copyright
© The Author(s), 2022. Published by Cambridge University Press

Footnotes

We are grateful for the comments of the Editor, a Co-Editor, four referees, and the participants of the “High Voltage Econometrics” workshop, which helped to improve the previous version of the manuscript.

References

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