This paper deals with the local asymptotic structure, in the sense ofLe Cam’s asymptotic theory of statistical experiments, of the signal detectionproblem in high dimension. More precisely, we consider the problemof testing the null hypothesis of sphericity of a high-dimensional...

This paper studies the asymptotic power of tests of sphericity against perturbations in a single unknown direction as both the dimensionality of the data and the number of observations go to infinity. We establish the convergence, under the null hypothesis and the alternative, of the log ratio...