On the detection of low rank matrices in the high-dimensional regime

Abstract : We address the detection of a low rank nxn matrix X0 from the noisy observation X0+Z for large n, where Z is a complex Gaussian random matrix with independent identically distributed Nc(0, 1/n) entries. Thanks to large random matrix theory results, it is now well-known that if the largest singular value lambda1(X0) of X0 verifies lambda1(X0) > 1, then it is possible to exhibit consistent tests. In this contribution, we prove a contrario that under the condition lambda1(X0) < 1, there are no consistent tests. Our proof is inspired by previous works devoted to the case of rank 1 matrices X0.
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Submitted on : Wednesday, August 29, 2018 - 3:09:13 PM
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Antoine Chevreuil, Philippe Loubaton. On the detection of low rank matrices in the high-dimensional regime. EUSIPCO, Sep 2018, Rome, Italy. ⟨hal-01798530v2⟩

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