High-dimensional change-point detection with sparse alternatives

We consider the problem of detection of a simultaneous change in mean in a sequence of Gaussian vectors. We assume that the change occurs only in some of the components of the vector. We construct a procedure of testing the change in mean adaptive to the number of non-zero components. Under the assumption that the vector dimension tends to infinity and the length of the sequence grows slower than the dimension of the signal we obtain the detection boundary for the test and show its rate-optimality.