5 research outputs found
Tests alternative to higher criticism for high-dimensional means under sparsity and column-wise dependence
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.Comment: 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
Multidimensional two-component Gaussian mixtures detection
International audienceLet be a -dimensional i.i.d sample from a distribution with density . The problem of detection of a two-component mixture is considered. Our aim is to decide whether is the density of a standard Gaussian random -vector () against is a two-component mixture: where are unknown parameters. Optimal separation conditions on and the dimension are established, allowing to separate both hypotheses with prescribed errors. Several testing procedures are proposed and two alternative subsets are considered