This work is concerned with tests for one-sample mean vectors under high dimensional cases. Existing high dimensional tests for mean vectors base on the assumption of elliptical distribution have been proposed recently. To extend to more distributions, we propose a signed-rank-based test. The proposed test statistic is robust and scalar-invariant. Asymptotic properties of the test statistic are established. Numerical studies show that the proposed test has a good control of the type-I error and is more efficiency. We also employ the proposed method to analyze an ophthalmic data.
LIU Yan
,
LI Shiming
,
ZHANG Sanguo
. Signed-rank-based test for high dimensional mean vector[J]. Journal of University of Chinese Academy of Sciences, 2022
, 39(5)
: 586
-592
.
DOI: 10.7523/j.ucas.2020.0059
[1] Bai Z D, Hewa S. Effect of high dimension:by an example of a two sample problem[J]. Statistica Sinica, 1996, 6(2):311-329.
[2] Chen S X, Qin Y L. A two sample test for high dimensional data with applications to gene-set testing[J]. Annals of Statistics, 2010, 38(2):808-835.DOI:10.1214/09-aos716.
[3] Srivastava M S, Meng D. A test for the mean vector with fewer observations than the dimension[J]. Journal of Multivariate Analysis, 2008, 99(3):386-402.DOI:10.1016/j.jmva.2006.11.002.
[4] Srivastava M S. A test for the mean vector with fewer observations than the dimension under non-normality[J]. Journal of Multivariate Analysis, 2009, 100(3):518-532.DOI:10.1016/j.jmva.2008.06.006.
[5] Srivastava M S, Shota K, Yutaka K. A two sample test in high dimensional data[J]. Journal of Multivariate Analysis, 2013, 114:349-358.DOI:10.1016/j.jmva.2012.08.014.
[6] Park J Y, Deepak N A. A test for the mean vector in large dimension and small samples[J]. Journal of Statistical Planning and Inference, 2013, 143(5):929-943.DOI:10.1016/j.jspi.2012.11.001.
[7] Wang L, Peng B, Li R Z. A high-dimensional nonparametric multivariate test for mean vector[J]. Journal of the American Statistical Association, 2015, 110(512):1658-1669.DOI:10.1080/01621459.2014.988215.
[8] Feng L, Zou C L, Wang Z J. Multivariate-sign-based high-dimensional tests for the two-sample location problem[J]. Journal of the American Statistical Association, 2016, 111(514):721-735.DOI:10.1080/01621459.2015.1035380.
