Power in high-dimensional testing problems
Journal
Econometrica
Type
journal article
Date Issued
2019
Author(s)
Kock, Anders Bredahl
;
Preinerstorfer, David
Abstract
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.
Language
English
Keywords
High-dimensional testing problems
power enhancement principle
power enhancement component
asymptotic enhanceability
marginal LAN
Refereed
Yes
Volume
87
Number
3
Start page
1055
End page
1069
Subject(s)
Eprints ID
266211