scholarly journals Asymptotic Expansion of the Misclassification Probabilities of D- and A-Criteria for Discrimination from Two High Dimensional Populations Using the Theory of Large Dimensional Random Matrices

1993 ◽  
Vol 46 (1) ◽  
pp. 154-174 ◽  
Author(s):  
H. Saranadasa
Keyword(s):  
Asymptotic Expansion ◽  
Random Matrices ◽  
High Dimensional

scholarly journals Small-Deviation Inequalities for Sums of Random Matrices

Symmetry ◽  
2019 ◽  
Vol 11 (5) ◽  
pp. 638
Author(s):  
Xianjie Gao ◽  
Chao Zhang ◽  
Hongwei Zhang
Keyword(s):  
Random Matrices ◽  
Large Deviation ◽  
Small Deviation ◽  
High Dimensional ◽  
Main Research ◽  
Infinite Dimensional ◽  
The Matrix ◽  
Largest Eigenvalues ◽  
Deviation Inequalities ◽  
Eigenvalues Of Random Matrices

Random matrices have played an important role in many fields including machine learning, quantum information theory, and optimization. One of the main research focuses is on the deviation inequalities for eigenvalues of random matrices. Although there are intensive studies on the large-deviation inequalities for random matrices, only a few works discuss the small-deviation behavior of random matrices. In this paper, we present the small-deviation inequalities for the largest eigenvalues of sums of random matrices. Since the resulting inequalities are independent of the matrix dimension, they are applicable to high-dimensional and even the infinite-dimensional cases.

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.

Sign in / Sign up

Export Citation Format

Share Document