Noureddine El Karoui

Primary Research Area: 
Applied & Theoretical Statistics
Applied Statistics, Theory of Statistics
Research Interests: 
High-dimensional statistics, random matrices, high-dimensional robust regression, high-dimensional M-estimation, the bootstrap and resampling in high-dimension, limit theorems and statistical inference, applied statistics
nkaroui [at] berkeley [dot] edu
Office / Location: 
311 Evans Hall

Brief bio:

I did my undergraduate studies at Ecole Polytechnique, in France, majoring in Applied Mathematics. I then studied at Stanford, where I got a PhD in Statistics (co-advised by David Donoho and Iain Johnstone) and a Master's in Financial Mathematics. 

My research has been supported by NSF grants (including a CAREER grant) and a Sloan research fellowship. I am grateful for their support. 

Select Publications: 
  •  Tracy-Widom limit for the largest eigenvalue of a large class of complex sample covariance matrices,The Annals of Probabililty,35(2): 663--714, March 07
  •  A rate of convergence result for the largest eigenvalue of complex white Wishart matrices, The Annals of Probability, 34(6):2077--2117, November 06
  •  Recent results about the largest eigenvalue of random covariance matrices and statistical application, Acta Physica Polonica B, 36(9):2681-2697, September 2005
  •  Getting more from digital SNP data (With Wei Zhou and Alice Whittemore),Statistics in Medicine     25:3124-3133, September 2006
  •  On the largest eigenvalue of Wishart matrices when n,p and p/n tend to infinity, Unpublished, Available on
  •  Spectrum estimation for large dimensional covariance matrices using random matrix theory, Annals of Statistics, 36(6): 2757-2790, December 2008
  •  Operator norm consistent estimation of large dimensional sparse covariance matrices, Annals of Statistics, 36(6): 2717-2756, December 2008
  •  Concentration of measure and spectra of random matrices: applications to correlation matrices, elliptical distributions and beyond, Annals of Applied Probability, 19(6):2362-2405, December 2009
  •  The spectrum of kernel random matrices, Annals of Statistics, 38(1): 1-51, February 2010
  •  High-dimensionality effects in the Markowitz problem and other quadratic programs with linear constraints: risk underestimation, Annals of Statistics, 38(10):3487–3566, December 2010
  •  On information plus noise kernel random matrices, Annals of Statistics, 38(10):3191–3216, October 2010
  •  Chapter « Random matrix Theory », Encyclopedia of Quantitative Finance, Publisher : Wiley, Editor : Rama Cont
  •  Chapter « Multivariate Statistics », Handbook of Random Matrix Theory, Publisher: Oxford; Editors: G. Akemann, J. Baik,, P. Di Francesco
  •  On the realized risk of Markowitz portfolios, to appear in SIAM Journal in Financial Engineering
  •  Second order accurate distributed eigenvector computation for extremely large matrices (with Alexandre d’Aspremont), Electronic Journal of Statistics, 4(2010), 1345-1385
  • Geometric sensitivity of random matrix results: consequences for shrinkage estimators of covariance and related statistical methods, (with Holger Koesters); under revision (67 pages)
  •  Weak  recovery conditions from graph portioning bounds and order statistics (with Alexandre d’Aspremont), Mathematics of Operations Research, 38,(2); 228-247, May 2013
  •  On robust regression with high-dimensional predictors (with Bean, Bickel,Lim and Yu), PNAS, 2013 110 (36) (August, 2013) 14557-14562
  •  Optimal M-estimation in high-dimensional regression (with Bean, Bickel and Yu), PNAS, 2013 110 (36) (August, 2013) 14563-14568
  •  Optimizing Automated Classification of Periodic Variable Stars in New Synoptic Surveys (with Long (1st author), Rice, Richards, Bloom), Publications of the Astronomical Society of the Pacific, 124 (913); March 2012, 280-295
  •  Estimation error reduction in portfolio optimization with Conditional Value-at-Risk (with Andrew Lim and Gah-Yi Vahn), 2nd round of revision, Management Science (33 pages)
  • A stochastic smoothing algorithm for semi-definite programming (with Alexandre d’Aspremont), SIAM Journal in Optimization 2014, 24 (3), pp. 1138-117
  •  Asymptotic behavior of unregularized and ridge-regularized high-dimensional robust regression estimators : rigorous results; Arxiv: 1311.2445 Under revision. 
  •  Vector diffusion maps and random matrices with random blocks (with Hau-tieng Wu);  Information and Inference (arXiv:1310.0188)
  •  Kernel density estimation with Berkson error (with Long(1st author) and Rice); Submitted  (arXiv:1401.3362)
  • Graph  Connection Laplacian methods can be made robust to noise (with Hau-tieng Wu); To appear in Annals of Statistics (arXiv:1405.6231)
  • Can we trust the bootstrap in high-dimension? (with Elizabeth Purdom); Submitted
  • On the impact of predictor geometry on the performance of high-dimensional ridge-regularized  generalized robust regression estimators; Submitted
  • The bootstrap, covariance matrices, and PCA in moderate and high-dimensions (with Elizabeth Purdom); Submitted