Robust test for detecting a signal in a high dimensional sparse
normal vector
Dr. Jun Park
Department of Mathematics and Statistics
University of Maryland, Baltimore County
Abstract
We consider the problem of testing whether a high
dimensional observation vector has signal, i.e., testing all the mean
values are zero versus the alternative that non-zero means exist.
The setup is when the dimension of vector is large, and the mean vector
is `sparse', e.g., the small fraction of mean values is non-zero.
We suggest a test which is not sensitive to the exact tail behavior under
normality assumption. In particular, if the `moderate
deviation' tail of the distribution is represented as the
product of a tail of a standard normal and a `slowly changing' function,
our suggested test is robust. In particular, a need for robust test is
expected when the observations are of the normalized form where normality
assumption is commonly used from C.L.T.