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

@article{Banerjee2018AsymptoticNA, title={Asymptotic normality and analysis of variance of log-likelihood ratios in spiked random matrix models}, author={Debapratim Banerjee and Zongming Ma}, journal={ArXiv}, year={2018}, volume={abs/1804.00567} }

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…

## 6 Citations

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The fundamental limits of detecting the presence of an additive rank-one perturbation to a Wigner matrix are studied and it is proved that the log-likelihood ratio of the spiked model against the nonspiked one is asymptotically normal below a certain reconstruction threshold, and that it is degenerate above.

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