Weak Detection in the Spiked Wigner Model with General Rank

Abstract

We study the statistical decision process of detecting the signal from a `signal+noise' type matrix model with an additive Wigner noise. We propose a hypothesis test based on the linear spectral statistics of the data matrix, which does not depend on the distribution of the signal or the noise. The test is optimal under the Gaussian noise if the signal-to-noise ratio is small, as it minimizes the sum of the Type-I and Type-II errors. Under the non-Gaussian noise, the test can be improved with an entrywise transformation to the data matrix. We also introduce an algorithm that estimates the rank of the signal when it is not known a priori.

arXiv comment35 pages, 3 figures

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Cited by in corpus (4)

• Weak detection in the spiked Wigner model
• Detection of Signal in the Spiked Rectangular Models
• Fluctuations of the Stieltjes transform of the empirical spectral distribution of selfadjoint polynomials in Wigner and deterministic diagonal matrices
• Precise Error Rates for Computationally Efficient Testing