On Identity Tests for High Dimensional Data Using RMT
Abstract
In this work, we redefined two important statistics, the CLRT test (Bai et.al., Ann. Stat. 37 (2009) 3822-3840) and the LW test (Ledoit and Wolf, Ann. Stat. 30 (2002) 1081-1102) on identity tests for high dimensional data using random matrix theories. Compared with existing CLRT and LW tests, the new tests can accommodate data which has unknown means and non-Gaussian distributions. Simulations demonstrate that the new tests have good properties in terms of size and power. What is more, even for Gaussian data, our new tests perform favorably in comparison to existing tests. Finally, we find the CLRT is more sensitive to eigenvalues less than 1 while the LW test has more advantages in relation to detecting eigenvalues larger than 1.
Keywords
Cite
@article{arxiv.1203.3278,
title = {On Identity Tests for High Dimensional Data Using RMT},
author = {Cheng Wang and Jing Yang and Baiqi Miao and Longbing Cao},
journal= {arXiv preprint arXiv:1203.3278},
year = {2013}
}
Comments
16 pages, 2 figures, 3 tables, To be published in the Journal of Multivariate Analysis