This review covers recent results concerning the estimation of large covariance matrices
using tools from Random Matrix Theory (RMT). We introduce several RMT methods and …

Portfolio optimization can be roughly categorized as the mean-variance approach and the
exponential growth rate approach based on different theoretical foundations, trading logics …

We consider the linear model $\vy=\vX\vbeta_ {\star}+\vepsilon $ with $\vX\in\mathbb
{R}^{n\times p} $ in the overparameterized regime $ p> n $. We estimate $\vbeta_ {\star} …

Second moments of asset returns are important for risk management and portfolio selection.
The problem of estimating second moments can be approached from two angles: time series …

We provide a unified analysis of the predictive risk of ridge regression and regularized
discriminant analysis in a dense random effects model. We work in a high-dimensional …

The aim of this book is to investigate the spectral properties of random matrices (RM) when
their dimensions tend to infinity. All classical limiting theorems in statistics are under the …

The idea for this book came from the time the authors spent at the Statistics and Applied
Mathematical Sciences Institute (SAMSI) in Research Triangle Park in North Carolina …

Random matrix theory has found many applications in physics, statistics and engineering
since its inception. Although early developments were motivated by practical experimental …

Nonlinear shrinkage estimation of large-dimensional covariance matrices Page 1 The Annals
of Statistics 2012, Vol. 40, No. 2, 1024–1060 DOI: 10.1214/12-AOS989 © Institute of …

We consider the eigenvalues and eigenvectors of finite, low rank perturbations of random
matrices. Specifically, we prove almost sure convergence of the extreme eigenvalues and …