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We also introduce an analogue of the Gaussian white noise model and show that if the population covariance is embeddable in that model and well-conditioned, then the banded approximations produce consistent estimates of the eigenvalues and associated eigenvectors of the covariance matrix. The results can be extended to smooth versions of banding and to non-Gaussian distributions with sufficiently short tails. A resampling approach is proposed for choosing the banding parameter in practice. This approach is illustrated numerically on both simulated and real data.<\/jats:p>","DOI":"10.1214\/009053607000000758","type":"journal-article","created":{"date-parts":[[2008,3,5]],"date-time":"2008-03-05T13:01:04Z","timestamp":1204722064000},"page":"199-227","source":"Crossref","is-referenced-by-count":923,"title":["Regularized estimation of large covariance matrices"],"prefix":"10.1214","volume":"36","author":[{"given":"Peter J.","family":"Bickel","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Elizaveta","family":"Levina","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"108","reference":[{"key":"17","doi-asserted-by":"publisher","unstructured":"Hoerl, A. E. and Kennard, R. W. (1970). 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