Linear Hypothesis Testing in Linear Models With High-Dimensional Responses

References

• Aoshima, M., and Yata, K. (2018), “Two-Sample Tests for High-Dimension, Strongly Spiked Eigenvalue Models,” Statistica Sinica, 28, 43–62. DOI: 10.5705/ss.202016.0063.
   Web of Science ®Google Scholar
• Ashburner, M., Ball, C. A., Blake, J. A., Botstein, D., Butler, H., Cherry, J. M., Davis, A. P., Dolinski, K., Dwight, S. S., Eppig, J. T., and Harris, M. A. (2000), “Gene Ontology: Tool for the Unification of Biology,” Nature Genetics, 25, 25–29. DOI: 10.1038/75556.
   PubMed Web of Science ®Google Scholar
• Bai, Z., and Saranadasa, H. (1996), “Effect of High Dimension: By an Example of a Two Sample Problem,” Statistica Sinica, 6, 311–329.
   Web of Science ®Google Scholar
• Baik, J., and Silverstein, J. W. (2006), “Eigenvalues of Large Sample Covariance Matrices of Spiked Population Models,” Journal of Multivariate Analysis, 97, 1382–1408. DOI: 10.1016/j.jmva.2005.08.003.
   Web of Science ®Google Scholar
• Benjamini, Y., and Hochberg, Y. (1995), “Controlling the False Discovery Rate: A Practical and Powerful Approach to Multiple Testing,” Journal of the Royal Statistical Society, Series B, 57, 289–300. DOI: 10.1111/j.2517-6161.1995.tb02031.x.
   Web of Science ®Google Scholar
• Benjamini, Y., and Yekutieli, D. (2001), “The Control of the False Discovery Rate in Multiple Testing Under Dependency,” The Annals of Statistics, 29, 1165–1188. DOI: 10.1214/aos/1013699998.
   Web of Science ®Google Scholar
• Cai, T., Liu, W., and Xia, Y. (2014), “Two-Sample Test of High Dimensional Means Under Dependence,” Journal of the Royal Statistical Society, Series B, 76, 349–372. DOI: 10.1111/rssb.12034.
   Google Scholar
• Chen, S. X., Li, J., and Zhong, P.-S. (2019), “Two-Sample and ANOVA Tests for High Dimensional Means,” The Annals of Statistics, 47, 1443–1474. DOI: 10.1214/18-AOS1720.
   Web of Science ®Google Scholar
• Chen, S. X., and Qin, Y.-L. (2010), “A Two-Sample Test for High-Dimensional Data With Applications to Gene-Set Testing,” The Annals of Statistics, 38, 808–835. DOI: 10.1214/09-AOS716.
   Web of Science ®Google Scholar
• Donoho, D. L., Gavish, M., and Johnstone, I. M. (2018), “Optimal Shrinkage of Eigenvalues in the Spiked Covariance Model,” The Annals of Statistics, 46, 1742. DOI: 10.1214/17-AOS1601.
   PubMed Web of Science ®Google Scholar
• Fan, J., Liao, Y., and Yao, J. (2015), “Power Enhancement in High-Dimensional Cross-Sectional Tests,” Econometrica, 83, 1497–1541. DOI: 10.3982/ECTA12749.
   PubMed Web of Science ®Google Scholar
• He, Y., Jiang, T., Wen, J., and Xu, G. (2019), “Likelihood Ratio Test in Multivariate Linear Regression: From Low to High Dimension,” Statistica Sinica (accepted).
   Web of Science ®Google Scholar
• He, Y., Xu, G., Wu, C., and Pan, W. (2021), “Asymptotically Independent U-Statistics in High-Dimensional Testing,” The Annals of Statistics, 49, 154–181. DOI: 10.1214/20-AOS1951.
   PubMed Web of Science ®Google Scholar
• Hotelling, H. (1931), “The Generalization of Student’s Ratio,” The Annals of Mathematical Statistics, 2, 360–378. DOI: 10.1214/aoms/1177732979.
   Google Scholar
• Huang, Y. (2015), “Projection Test for High-Dimensional Mean Vectors With Optimal Direction,” Ph.D. dissertation, Department of Statistics, The Pennsylvania State University at University Park.
   Google Scholar
• Johnstone, I. M. (2001), “On the Distribution of the Largest Eigenvalue in Principal Components Analysis,” The Annals of Statistics, 29, 295–327. DOI: 10.1214/aos/1009210544.
   Web of Science ®Google Scholar
• Kock, A. B., and Preinerstorfer, D. (2019), “Power in High-Dimensional Testing Problems,” Econometrica, 87, 1055–1069. DOI: 10.3982/ECTA15844.
   Web of Science ®Google Scholar
• Lopes, M., Jacob, L., and Wainwright, M. J. (2011), “A More Powerful Two-Sample Test in High Dimensions Using Random Projection,” in Advances in Neural Information Processing Systems, pp. 1206–1214.
   Google Scholar
• Srivastava, M. S., and Du, M. (2008), “A Test for the Mean Vector With Fewer Observations Than the Dimension,” Journal of Multivariate Analysis, 99, 386–402. DOI: 10.1016/j.jmva.2006.11.002.
   Web of Science ®Google Scholar
• Srivastava, R., Li, P., and Ruppert, D. (2016), “RAPTT: An Exact Two-Sample Test in High Dimensions Using Random Projections,” Journal of Computational and Graphical Statistics, 25, 954–970. DOI: 10.1080/10618600.2015.1062771.
   Web of Science ®Google Scholar
• Thulin, M. (2014), “A High-Dimensional Two-Sample Test for the Mean Using Random Subspaces,” Computational Statistics & Data Analysis, 74, 26–38.
   Web of Science ®Google Scholar
• Tilton, S. C., Karin, N. J., Webb-Robertson, B.-J. M., Waters, K. M., Mikheev, V., Lee, K. M., Corley, R. A., Pounds, J. G., and Bigelow, D. J. (2013), “Impaired Transcriptional Response of the Murine Heart to Cigarette Smoke in the Setting of High Fat Diet and Obesity,” Chemical Research in Toxicology, 26, 1034–1042. DOI: 10.1021/tx400078b.
   PubMed Web of Science ®Google Scholar
• Wang, R., and Xu, X. (2018), “On Two-Sample Mean Tests Under Spiked Covariances,” Journal of Multivariate Analysis, 167, 225–249. DOI: 10.1016/j.jmva.2018.05.004.
   Web of Science ®Google Scholar
• Wang, W., and Fan, J. (2017), “Asymptotics of Empirical Eigenstructure for High Dimensional Spiked Covariance,” The Annals of Statistics, 45, 1342. DOI: 10.1214/16-AOS1487.
   PubMed Web of Science ®Google Scholar
• Xu, G., Lin, L., Wei, P., and Pan, W. (2016), “An Adaptive Two-Sample Test for High-Dimensional Means,” Biometrika, 103, 609–624. DOI: 10.1093/biomet/asw029.
   PubMed Web of Science ®Google Scholar
• Xue, K., and Yao, F. (2020), “Distribution and Correlation-Free Two-Sample Test of High-Dimensional Means,” The Annals of Statistics, 48, 1304–1328. DOI: 10.1214/19-AOS1848.
   Web of Science ®Google Scholar
• Zhang, J.-T., Guo, J., Zhou, B., and Cheng, M.-Y. (2020), “A Simple Two-Sample Test in High Dimensions Based on l2-Norm,” Journal of the American Statistical Association, 115, 1011–1027. DOI: 10.1080/01621459.2019.1604366.
   Web of Science ®Google Scholar