Asymptotic Normality of Log Likelihood Ratio and Fundamental Limit of the Weak Detection for Spiked Wigner Matrices

Autor:	Chung, Hye Won, Lee, Jiho, Lee, Ji Oon
Rok vydání:	2022
Předmět:	Mathematics - Statistics Theory Mathematics - Probability Statistics - Machine Learning 62H15 60F05 82B44
Druh dokumentu:	Working Paper
Popis:	We consider the problem of detecting the presence of a signal in a rank-one spiked Wigner model. For general non-Gaussian noise, assuming that the signal is drawn from the Rademacher prior, we prove that the log likelihood ratio (LR) of the spiked model against the null model converges to a Gaussian when the signal-to-noise ratio is below a certain threshold. The threshold is optimal in the sense that the reliable detection is possible by a transformed principal component analysis (PCA) above it. From the mean and the variance of the limiting Gaussian for the log-LR, we compute the limit of the sum of the Type-I error and the Type-II error of the likelihood ratio test. We also prove similar results for a rank-one spiked IID model where the noise is asymmetric but the signal is symmetric. Comment: 33 pages, 2 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2203.00821 Zobrazit plný text záznamu View this record from Arxiv