The geometry of invariants for generalized coherence tests

Abstract

This paper considers the problem of testing for mutual independence of multiple sets of complex Gaussian vectors. This problem has classical roots in statistics and has been of recent interest in the signal processing literature in connection with multi-channel signal detection. The maximal invariant statistic for this problem is described both as a collection of subspaces of the data space (i.e., points on a complex Grassmannian manifold) and as a corresponding set of complex matrices. The distribution of the maximal invariant is also derived under both hypotheses in the testing problem.