Weak detection in the spiked Wigner model
| Autor: | Hye Won Chung, Ji Oon Lee |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2018 |
| Předmět: |
FOS: Computer and information sciences
Computer Science - Machine Learning Probability (math.PR) Machine Learning (stat.ML) Mathematics - Statistics Theory Statistics Theory (math.ST) Library and Information Sciences Computer Science Applications Machine Learning (cs.LG) Statistics - Machine Learning FOS: Mathematics 62H15 60B20 Mathematics - Probability Information Systems |
| Popis: | We consider the weak detection problem in a rank-one spiked Wigner data matrix where the signal-to-noise ratio is small so that reliable detection is impossible. We propose a hypothesis test on the presence of the signal by utilizing the linear spectral statistics of the data matrix. The test is data-driven and does not require prior knowledge about the distribution of the signal or the noise. When the noise is Gaussian, the proposed test is optimal in the sense that its error matches that of the likelihood ratio test, which minimizes the sum of the Type-I and Type-II errors. If the density of the noise is known and non-Gaussian, the error of the test can be lowered by applying an entrywise transformation to the data matrix. We establish a central limit theorem for the linear spectral statistics of general rank-one spiked Wigner matrices as an intermediate step. 45 pages, 5 figures |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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