Optimal signal detection in some spiked random matrix models: Likelihood ratio tests and linear spectral statistics
尖峰随机矩阵模型中的最优信号检测：似然比检验与线性谱统计量
We study signal detection by likelihood ratio tests in a number of spiked random matrix models, including but not limited to Gaussian mixtures and spiked Wishart covariance matrices. We work directly with multi-spiked cases in these models and with flexible priors on signal components that allow dependence across spikes. We derive asymptotic normality for the log-likelihood ratios when the signal-to-noise ratios are below certain bounds. In addition, the log-likelihood…