References
- Donoho D, Jin J. Higher criticism for detecting sparse heterogeneous mixtures. Ann Statist. 2004;32:962–994. doi: 10.1214/009053604000000265
- Fan J, Li R. Variable selection via nonconcave penalized likelihood and its oracle properties. J Amer Statist Assoc. 2001;96:1348–1360. doi: 10.1198/016214501753382273
- Fan J, Lv J. Sure independence screening for ultrahigh dimensional feature space. J R Stat Soc Ser B Stat Methodol. 2008;70:849–911. doi: 10.1111/j.1467-9868.2008.00674.x
- Bai Z, Saranadasa H. Effect of high dimension: by an example of a two sample problem. Statist Sin. 1996;6:311–329.
- Chen SX, Qin YL. A two-sample test for high-dimensional data with applications to gene-set testing. Ann Statist. 2010;38:808–835. doi: 10.1214/09-AOS716
- Srivastava MS. A test for the mean vector with fewer observations than the dimension under non-normality. J Multivariate Anal. 2009;100:518–532. doi: 10.1016/j.jmva.2008.06.006
- Cai T, Liu W, Xia Y. Two sample test of high dimensional means under dependence. J R Stat Soc Ser B Statist Methodol. 2014;76:349–372. doi: 10.1111/rssb.12034
- Hallin M, Paindaveine D. Optimal tests for multivariate location based on interdirections and pseudo-Mahalanobis ranks. Ann Statist. 2002;30:1103–1133. doi: 10.1214/aos/1031689019
- Mahfoud ZR, Randles RH. On multivariate signed rank tests. J Nonparametr Stat. 2005;17:201–216. doi: 10.1080/1048525042000267806
- Paindaveine D, Verdebout T. On high-dimensional sign tests. Bernoulli. 2016;22:1745–1769. doi: 10.3150/15-BEJ710
- Wang L, Peng B, Li R. A high-dimensional nonparametric multivariate test for mean vector. J Amer Statist Assoc. 2015;110:1658–1669. doi: 10.1080/01621459.2014.988215
- Feng L, Zou C, Wang Z. Multivariate-sign-based high-dimensional tests for the two-sample location problem. J Amer Statist Assoc. 2016;111:721–735. doi: 10.1080/01621459.2015.1035380
- Li R, Huang Y, Wang L, et al. Projection test for high dimensional mean vectors with optimal direction. Manuscript. 2015.
- Oja H. Multivariate nonparametric methods with R: an approach based on spatial signs and ranks. New York: Springer Science and Business Media; 2010.
- Zou C, Peng L, Feng L, et al. Multivariate sign-based high-dimensional tests for sphericity. Biometrika. 2014;101:229–236. doi: 10.1093/biomet/ast040
- Wasserman L, Roeder K. High dimensional variable selection. Ann Statist. 2009;37:2178–2201. doi: 10.1214/08-AOS646
- Lopes M, Jacob L, Wainwright MJ. A more powerful two-sample test in high dimensions using random projection. Adv Neural Inf Process Syst. 2012;24:1206–1214.
- Lauter J. Exact t and F tests for analyzing studies with multiple endpoints. Biometrics. 1996;52:964–970. doi: 10.2307/2533057
- Ghosh BK. Sequential tests of statistical hypotheses. Ann Math Statist. 1970;42:1104–1156.
- Ghosh BK. Some monotonicity theorems for χ2, F and t distributions with applications. J R Stat Soc Ser B. 1973;35:480–492.
- Bickel PJ, Levina E. Covariance regularization by thresholding. Ann Statist. 2008;36:2577–2604. doi: 10.1214/08-AOS600
- Fan J, Liao Y, Mincheva M. Large covariance estimation by thresholding principal orthogonal complements. J R Stat Soc Ser B Stat Methodol. 2013;75:603–680. doi: 10.1111/rssb.12016