CREATES

TY - JOUR

T1 - Power in High-Dimensional Testing Problems

AU - Kock, Anders Bredahl

AU - Preinerstorfer, David

PY - 2019/5/1

Y1 - 2019/5/1

N2 - 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.

AB - 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.

KW - asymptotic enhanceability

KW - High-dimensional testing problems

KW - marginal LAN

KW - power enhancement component

KW - power enhancement principle

UR - http://www.scopus.com/inward/record.url?scp=85065905463&partnerID=8YFLogxK

U2 - 10.3982/ECTA15844

DO - 10.3982/ECTA15844

M3 - Journal article

AN - SCOPUS:85065905463

VL - 87

SP - 1055

EP - 1069

JO - Econometrica

JF - Econometrica

SN - 0012-9682

IS - 3

ER -