Abstract: This paper deals with the local asymptotic structure, in the sense of Le Cam���s asymptotic theory of statistical experiments, of the signal detection problem in high dimension. More precisely, we consider the problem of testing the null hypothesis of sphericity of a high-dimensional covariance matrix against an alternative of (unspecified) multiple symmetry-breaking directions (multispiked alternatives). Simple analytical expressions for the asymptotic power envelope and the asymptotic powers of previously proposed tests are derived. The...
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Artificial intelligence