246 citations · 782 across the 16 of their papers we have counts for
6 papers · 1 filter
High-dimensionality effects in the Markowitz problem and other quadratic programs with linear constraints: Risk underestimation
Noureddine El Karoui
We first study the properties of solutions of quadratic programs with linear equality constraints whose parameters are estimated from data in the high-dimensional setting where p,…
Geometric sensitivity of random matrix results: consequences for shrinkage estimators of covariance and related statistical methods
Noureddine El Karoui, Holger Koesters
Shrinkage estimators of covariance are an important tool in modern applied and theoretical statistics. They play a key role in regularized estimation problems, such as ridge regres…
On information plus noise kernel random matrices
Noureddine El Karoui
Kernel random matrices have attracted a lot of interest in recent years, from both practical and theoretical standpoints. Most of the theoretical work so far has focused on the cas…
Operator norm consistent estimation of large-dimensional sparse covariance matrices
Noureddine El Karoui
Estimating covariance matrices is a problem of fundamental importance in multivariate statistics. In practice it is increasingly frequent to work with data matrices of dimensio…
Spectrum estimation for large dimensional covariance matrices using random matrix theory
Noureddine El Karoui
Estimating the eigenvalues of a population covariance matrix from a sample covariance matrix is a problem of fundamental importance in multivariate statistics; the eigenvalues of c…
On the largest eigenvalue of Wishart matrices with identity covariance when n, p and p/n tend to infinity
Noureddine El Karoui
Let X be a n*p matrix and l_1 the largest eigenvalue of the covariance matrix X^{*}*X. The "null case" where X_{i,j} are independent Normal(0,1) is of particular interest for princ…