Two-Sample Covariance Matrix Testing and Support Recovery in High-Dimensional and Sparse Settings

REFERENCES

• Anderson , T. W. 2003 . An Introduction to Multivariate Statistical Analysis , (3rd ed.) , New York: Wiley-Interscience .
   Google Scholar
• Baraud , Y. 2002 . “Non-Asymptotic Minimax Rates of Testing in Signal Detection,” . Bernoulli , 8 : 577 – 606 .
   Web of Science ®Google Scholar
• Berman , S. M. 1962 . “A Law of Large Numbers for the Maximum of a Stationary Gaussian Sequence,” . The Annals of Mathematical Statistics , 33 : 894 – 908 .
   Google Scholar
• Cai , T. and Jiang , T. 2011 . “Limiting Laws of Coherence of Random Matrices With Applications to Testing Covariance Structure and Construction of Compressed Sensing Matrices,” . The Annals of Statistics , 39 : 1496 – 1525 .
   Web of Science ®Google Scholar
• Cai , T. and Jiang , T. 2012 . “Phase Transition in Limiting Distributions of Coherence of High-Dimensional Random Matrices,” . Journal of Multivariate Analysis , 107 : 24 – 39 .
   Web of Science ®Google Scholar
• Cai , T. and Liu , W. D. 2011 . “Adaptive Thresholding for Sparse Covariance Matrix Estimation,” . Journal of the American Statistical Association , 106 : 672 – 684 .
   Web of Science ®Google Scholar
• Cai , T. , Liu , W. D. and Xia , Y. 2012 . Supplement to “Two-Sample Covariance Matrix Testing and Support Recovery in High-Dimensional and Sparse Settings,” . Technical Report
   Google Scholar
• de la Fuente , A. 2010 . “From ‘Differential Expression’ to ‘Differential Networking’-Identification of Dysfunctional Regulatory Networks in Diseases,” . Trends in Genetics , 26 : 326 – 333 .
   PubMed Web of Science ®Google Scholar
• Gupta , A. K. and Tang , J. 1984 . “Distribution of Likelihood Ratio Statistic for Testing Equality of Covariance Matrices of Multivariate Gaussian Models,” . Biometrika , 71 : 555 – 559 .
   Web of Science ®Google Scholar
• Gupta , D. S. and Giri , N. 1973 . “Properties of Tests Concerning Covariance Matrices of Normal Distributions,” . The Annals of Statistics , 6 : 1222 – 1224 .
   Google Scholar
• Ho , J. W. , Stefani , M. , dos Remedios , C. G. and Charleston , M. A. 2008 . “Differential Variability Analysis of Gene Expression and its Application to Human Diseases,” . Bioinformatics , 24 : 390 – 398 .
   Web of Science ®Google Scholar
• Hu , R. , Qiu , X. and Glazko , G. 2010 . “A New Gene Selection Procedure Based on the Covariance Distance,” . Bioinformatics , 26 : 348 – 354 .
   PubMed Web of Science ®Google Scholar
• Hu , R. , Qiu , X. , Glazko , G. , Klevanov , L. and Yakovlev , A. 2009 . “Detecting Intergene Correlation Changes in Microarray Analysis: A New Approach to Gene Selection,” . BMC Bioinformatics , 10 : 20
   PubMed Web of Science ®Google Scholar
• Jiang , T. 2004 . “The Asymptotic Distributions of the Largest Entries of Sample Correlation Matrices,” . The Annals of Applied Probability , 14 : 865 – 880 .
   Web of Science ®Google Scholar
• Li , J. and Chen , S. 2012 . “Two Sample Tests for High Dimensional Covariance Matrices,” . The Annals of Statistics , 40 : 908 – 940 .
   Web of Science ®Google Scholar
• Liu , W. , Lin , Z. Y. and Shao , Q. M. 2008 . “The Asymptotic Distribution and Berry-Esseen Bound of a New Test for Independence in High Dimension With an Application to Stochastic Optimization,” . The Annals of Applied Probability , 18 : 2337 – 2366 .
   Web of Science ®Google Scholar
• O’Brien , P. C. 1992 . “Robust Procedures for Testing Equality of Covariance Matrices,” . Biometrics , 48 : 819 – 827 .
   Web of Science ®Google Scholar
• Perlman , M. D. 1980 . “Unbiasedness of the Likelihood Ratio Tests for Equality of Several Covariance Matrices and Equality of Several Multivariate Normal Populations,” . The Annals of Statistics , 8 : 247 – 263 .
   Web of Science ®Google Scholar
• Schott , J. R. 2007 . “A Test for the Equality of Covariance Matrices When the Dimension is Large Relative to the Sample Sizes,” . Computational Statistics and Data Analysis , 51 : 6535 – 6542 .
   Web of Science ®Google Scholar
• Singh , D. , Febbo , P. , Ross , K. , Jackson , D. , Manola , J. , Ladd , C. , Tamayo , P. , Renshaw , A. , D′Amico , A. and Richie , J. 2002 . “Gene Expression Correlates of Clinical Prostate Cancer Behavior,” . Cancer Cell , 1 : 203 – 209 .
   PubMed Web of Science ®Google Scholar
• Srivastava , M. S. and Yanagihara , H. 2010 . “Testing the Equality of Several Covariance Matrices With Fewer Observations Than the Dimension,” . Journal of Multivariate Analysis , 101 : 1319 – 1329 .
   Web of Science ®Google Scholar
• Sugiura , N. and Nagao , H. 1968 . “Unbiasedness of Some Test Criteria for the Equality of One or Two Covariance Matrices,” . The Annals of Mathematical Statistics , 39 : 1682 – 1692 .
   Google Scholar
• Xu , P. , Brock , G. N. and Parrish , R. S. 2009 . “Modified Linear Discriminant Analysis Approaches for Classification of High-Dimensional Microarray Data,” . Computational Statistics and Data Analysis , 53 : 1674 – 1687 .
   Web of Science ®Google Scholar
• Zaïtsev , A. Yu . 1987 . “On the Gaussian Approximation of Convolutions Under Multidimensional Analogues of S.N. Bernstein’s Inequality Conditions,” . Probability Theory and Related Fields , 74 : 535 – 566 .
   Web of Science ®Google Scholar
• Zhou , W. 2007 . “Asymptotic Distribution of the Largest Off-Diagonal Entry of Correlation Matrices,” . Transactions of the American Mathematical Society , 359 : 5345 – 5364 .
   Web of Science ®Google Scholar