On the detection of low rank matrices in the high-dimensional regime
Year: 2018
Type: article
Abstract: We address the detection of a low rank n×n matrix X 0 from the noisy observation X 0 +Z when n → ∞, where Z is a complex Gaussian random matrix with independent identically distributed ℕ c (0, [1/n]) entries. Thanks to large random matrix theory results, it is now well-known that if the largest singular value λ 1 (X 0 ) of X 0 verifies λ 1 (X 0 ) > 1, then it is possible to exhibit consistent tests. In this contribution, we prove a contrario that under the condition λ 1 (X 0 ) <; 1, there are no consistent tests. Our proof is inspired by previous works devoted to the case of rank 1 matrices X 0 .
Source: HAL
Authors: Chevreuil, Antoine, Loubaton, Philippe
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2964182021