Work

Optimal signal detection in some spiked random matrix models: Likelihood ratio tests and linear spectral statistics

Year: 2022

Type: article

Abstract: 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.

Source: The Annals of Statistics

DOI: 10.1214/21-aos2150

Authors: Debapratim Banerjee, Zongming Ma

Institution: University of Pennsylvania

Language: English

Topic: Random Matrices and Applications

Subfield: Statistics and Probability

Field: Mathematics

Domain: Physical Sciences

Open Access status: bronze

Funder: National Science Foundation

Award: CAREER: Nonparametric Eigenanalysis of High Dimensional Data