A CLT for regularized sample covariance matrices

Greg W. Anderson, Ofer Zeitouni

Research output: Contribution to journalArticlepeer-review

9 Scopus citations


We consider the spectral properties of a class of regularized estimators of (large) empirical covariance matrices corresponding to stationary (but not necessarily Gaussian) sequences, obtained by banding. We prove a law of large numbers (similar to that proved in the Gaussian case by Bickel and Levina), which implies that the spectrum of a banded empirical covariance matrix is an efficient estimator. Our main result is a central limit theorem in the same regime, which to our knowledge is new, even in the Gaussian setup.

Original languageEnglish (US)
Pages (from-to)2553-2576
Number of pages24
JournalAnnals of Statistics
Issue number6
StatePublished - Dec 2008


  • Random matrices
  • Regularization
  • Sample covariance


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