Optimal signal detection in some spiked random matrix models: Likelihood ratio tests and linear spectral statistics
研究了高斯混合和尖峰Wishart协方差矩阵等模型中，通过似然比检验进行信号检测，推导了对数似然比的渐近正态性，并证明在信噪比低于某界限时，可用线性谱统计实现渐近最优检验功效。
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 ratios can be asymptotically decomposed as weighted sums of a collection of statistics which we call bipartite signed cycles. Based on this decomposition, we show that below the bounds we could always achieve the asymptotically optimal powers of likelihood ratio tests via tests based on linear spectral statistics which have polynomial time complexity.