Testing the independence of sets of largedimensional variables
 DanDan Jiang,
 ZhiDong Bai,
 ShuRong Zheng
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Abstract
This paper proposes the corrected likelihood ratio test (LRT) and largedimensional trace criterion to test the independence of two large sets of multivariate variables of dimensions p _{1} and p _{2} when the dimensions p = p _{1} + p _{2} and the sample size n tend to infinity simultaneously and proportionally. Both theoretical and simulation results demonstrate that the traditional χ ^{2} approximation of the LRT performs poorly when the dimension p is large relative to the sample size n, while the corrected LRT and largedimensional trace criterion behave well when the dimension is either small or large relative to the sample size. Moreover, the trace criterion can be used in the case of p > n, while the corrected LRT is unfeasible due to the loss of definition.
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 Title
 Testing the independence of sets of largedimensional variables
 Journal

Science China Mathematics
Volume 56, Issue 1 , pp 135147
 Cover Date
 20130101
 DOI
 10.1007/s1142501245010
 Print ISSN
 16747283
 Online ISSN
 18691862
 Publisher
 SP Science China Press
 Additional Links
 Topics
 Keywords

 largedimensional data analysis
 independence test
 random Fmatrices
 15A52
 62H15
 60F05
 62E20
 15A18
 Authors

 DanDan Jiang ^{(1)}
 ZhiDong Bai ^{(2)}
 ShuRong Zheng ^{(2)}
 Author Affiliations

 1. School of Mathematics, Jilin University, Changchun, 130012, China
 2. KLAS and School of Mathematics and Statistics, Northeast Normal University, Changchun, 130024, China