Journal club - Random matrix theory in statistics: A review

The article ”Random matrix theory in statistics: A review” was written by D. Paul and A. Aue and published in the Journal of Statistical Planning and Inference in 2015. Random Matrix Theory (RMT) is interested among other topics in describing the asymptotic behavior of the singular values and singular vectors of random matrices. Random matrices emerge in many statistical problems, that can be treated using results from random matrix theory. Applications include hypothesis testing, covariance estimation and dimensionality reduction. I present the most classical results reviewed by Paul & Aue and their application two three statistical problems. I focus on real-valued random matrices, but most of the results presented here hold for complex-valued matrices and their extensions can be found in the original paper.