Asymptotic normality and analysis of variance of log-likelihood ratios in spiked random matrix models

Abstract

The present manuscript studies 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 the signal component that allow dependence across spikes. We derive asymptotic normality for the log-likelihood ratios when the signal-to- noise ratios are below certain thresholds. In addition, we show that the variances of the log-likelihood ratios can be asymptotically decomposed as the sums of those of a collection of statistics which we call bipartite signed cycles.

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• Optimality and Sub-optimality of PCA for Spiked Random Matrices and Synchronization
• Optimal hypothesis testing for stochastic block models with growing degrees
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Cited by in corpus (3)

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