POWER IN HIGH-DIMENSIONAL TESTING PROBLEMS

Fan, Liao, and Yao (2015) recently introduced a remarkable method for increasing the asymptotic power of tests in high-dimensional testing problems. If applicable to a given test, their power enhancement principle leads to an improved test that has the same asymptotic size, has uniformly non-inferio...

Full description

Saved in:
Bibliographic Details
Published in:Econometrica 2019-05, Vol.87 (3), p.1055-1069
Main Authors: Kock, Anders Bredahl, Preinerstorfer, David
Format: Article
Language:English
Subjects:
asymptotic enhanceability
High‐dimensional testing problems
marginal LAN
Normality
NOTES AND COMMENTS
Power
power enhancement component
power enhancement principle
Research methodology
Sample size
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:Fan, Liao, and Yao (2015) recently introduced a remarkable method for increasing the asymptotic power of tests in high-dimensional testing problems. If applicable to a given test, their power enhancement principle leads to an improved test that has the same asymptotic size, has uniformly non-inferior asymptotic power, and is consistent against a strictly broader range of alternatives than the initially given test. We study under which conditions this method can be applied and show the following: In asymptotic regimes where the dimensionality of the parameter space is fixed as sample size increases, there often exist tests that cannot be further improved with the power enhancement principle. However, when the dimensionality of the parameter space increases sufficiently slowly with sample size and a marginal local asymptotic normality (LAN) condition is satisfied, every test with asymptotic size smaller than 1 can be improved with the power enhancement principle. While the marginal LAN condition alone does not allow one to extend the latter statement to all rates at which the dimensionality increases with sample size, we give sufficient conditions under which this is the case.
ISSN:0012-9682
1468-0262
DOI:10.3982/ECTA15844