The spiked Wigner model is a statistical model used to detect the presence of a signal in a noisy environment. It is particularly relevant in scenarios where the noise is non-Gaussian, and the signal is drawn from a Rademacher prior. The model involves a rank-one matrix with a signal component added to a Wigner matrix, which represents the noise. The challenge is to detect the signal when the signal-to-noise ratio (SNR) is below a certain threshold. Below this threshold, the log likelihood ratio (LR) of the spiked model against the null model converges to a Gaussian distribution. This threshold is considered optimal because reliable detection is possible using a transformed principal component analysis (PCA) above it. The model also provides insights into the sum of Type-I and Type-II errors of the likelihood ratio test, offering a comprehensive understanding of the detection capabilities in such noisy environments.
Transformed principal component analysis (PCA)
Rank-one spiked model
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Type-I and Type-II error rates
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No
No
Gaussian convergence of log likelihood ratio, optimal detection threshold
No
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No
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Detection threshold dependency
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No
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No
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No
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0.00
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01/01/1970
01/01/1970
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Yes