Tests alternative to higher criticism for high-dimensional means under sparsity and column-wise dependence
Abstract
We consider two alternative tests to the Higher Criticism test of Donoho and Jin [Ann. Statist. 32 (2004) 962-994] for high-dimensional means under the sparsity of the nonzero means for sub-Gaussian distributed data with unknown column-wise dependence. The two alternative test statistics are constructed by first thresholding and statistics based on the sample means, respectively, followed by maximizing over a range of thresholding levels to make the tests adaptive to the unknown signal strength and sparsity. The two alternative tests can attain the same detection boundary of the Higher Criticism test in [Ann. Statist. 32 (2004) 962-994] which was established for uncorrelated Gaussian data. It is demonstrated that the maximal -thresholding test is at least as powerful as the maximal -thresholding test, and both the maximal and -thresholding tests are at least as powerful as the Higher Criticism test.
Keywords
Cite
@article{arxiv.1312.5103,
title = {Tests alternative to higher criticism for high-dimensional means under sparsity and column-wise dependence},
author = {Ping-Shou Zhong and Song Xi Chen and Minya Xu},
journal= {arXiv preprint arXiv:1312.5103},
year = {2013}
}
Comments
Published in at http://dx.doi.org/10.1214/13-AOS1168 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)