OPTIMAL SIGNAL DETECTION IN SOME SPIKED RANDOM MATRIX MODELS: LIKELIHOOD RATIO TESTS AND LINEAR SPECTRAL STATISTICS
成果类型：
Article
署名作者：
Banerjee, Debapratim; Ma, Zongming
署名单位：
University of Pennsylvania
刊物名称：
ANNALS OF STATISTICS
ISSN/ISSBN：
0090-5364
DOI：
10.1214/21-AOS2150
发表日期：
2022
页码：
1910-1932
关键词：
摘要：
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.