scholarly journals Correction to: Asymptotic Normality for Inference on Multisample, High-Dimensional Mean Vectors Under Mild Conditions

2021 ◽  
Author(s):  
Makoto Aoshima ◽  
Kazuyoshi Yata
Keyword(s):  
Asymptotic Normality ◽  
High Dimensional ◽  
Mild Conditions ◽  
Mean Vectors

scholarly journals Power in High‐Dimensional Testing Problems

Econometrica ◽  
2019 ◽  
Vol 87 (3) ◽  
pp. 1055-1069 ◽  
Author(s):  
Anders Bredahl Kock ◽  
David Preinerstorfer
Keyword(s):  
Asymptotic Normality ◽  
Sample Size ◽  
Parameter Space ◽  
Sufficient Conditions ◽  
High Dimensional ◽  
Local Asymptotic Normality ◽  
Asymptotic Power ◽  
Asymptotic Size ◽  
Power Of Tests ◽  
Power Enhancement

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.

An adaptive spatial-sign-based test for mean vectors of elliptically distributed high-dimensional data

2019 ◽  
Vol 12 (1) ◽  
pp. 93-106
Author(s):  
Bu Zhou ◽  
Jia Guo ◽  
Jianwei Chen ◽  
Jin-Ting Zhang
Keyword(s):  
High Dimensional Data ◽  
High Dimensional ◽  
Mean Vectors

High-dimensional two-sample mean vectors test and support recovery with factor adjustment

2020 ◽  
Vol 151 ◽  
pp. 107004
Author(s):  
Yong He ◽  
Mingjuan Zhang ◽  
Xinsheng Zhang ◽  
Wang Zhou
Keyword(s):  
High Dimensional ◽  
Sample Mean ◽  
Mean Vectors ◽  
Support Recovery

Ridgelized Hotelling’s T2 test on mean vectors of large dimension

2021 ◽  
pp. 2250011
Author(s):  
Gao-Fan Ha ◽  
Qiuyan Zhang ◽  
Zhidong Bai ◽  
You-Gan Wang
Keyword(s):  
Random Matrices ◽  
Pathway Analysis ◽  
Large Dimension ◽  
High Dimensional ◽  
Stat Assoc ◽  
Moment Conditions ◽  
Local Statistics ◽  
Mean Vectors ◽  
Simulation Results ◽  
Mean Vector

In this paper, a ridgelized Hotelling’s [Formula: see text] test is developed for a hypothesis on a large-dimensional mean vector under certain moment conditions. It generalizes the main result of Chen et al. [A regularized Hotelling’s [Formula: see text] test for pathway analysis in proteomic studies, J. Am. Stat. Assoc. 106(496) (2011) 1345–1360.] by relaxing their Gaussian assumption. This is achieved by establishing an exact four-moment theorem that is a simplified version of Tao and Vu’s [Random matrices: universality of local statistics of eigenvalues, Ann. Probab. 40(3) (2012) 1285–1315] work. Simulation results demonstrate the superiority of the proposed test over the traditional Hotelling’s [Formula: see text] test and its several extensions in high-dimensional situations.

scholarly journals On testing the equality of high dimensional mean vectors with unequal covariance matrices

2015 ◽  
Vol 69 (2) ◽  
pp. 365-387 ◽  
Author(s):  
Jiang Hu ◽  
Zhidong Bai ◽  
Chen Wang ◽  
Wei Wang
Keyword(s):  
Covariance Matrices ◽  
High Dimensional ◽  
Mean Vectors

Robust two-sample test of high-dimensional mean vectors under dependence

2019 ◽  
Vol 169 ◽  
pp. 312-329
Author(s):  
Wei Wang ◽  
Nan Lin ◽  
Xiang Tang
Keyword(s):  
High Dimensional ◽  
Sample Test ◽  
Mean Vectors
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