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

2018/04/02 by Debapratim Banerjee, Banerjee, Debapratim, Zongming Ma +1 · 1 citation
Mathematics · #Advanced Algebra and Geometry #FOS: Computer and information sciences #FOS: Mathematics #Information Theory (cs.IT) #Probability (math.PR) #Random Matrices and Applications #Statistics Theory (math.ST) #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.1804.00567

openalex publication_date 2018/04/02 · openalex created_date 2018/04/13 · openalex updated_date 2026/07/28

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.

Citations

• Optimality and Sub-optimality of PCA for Spiked Random Matrices and Synchronization
• Optimal hypothesis testing for stochastic block models with growing degrees
• Detection limits in the high-dimensional spiked rectangular model

Cited by

• Contextual Stochastic Block Model: Sharp Thresholds and Contiguity

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