2 research outputs found
Spectrum Estimation: A Unified Framework for Covariance Matrix Estimation and PCA in Large Dimensions
Covariance matrix estimation and principal component analysis (PCA) are two
cornerstones of multivariate analysis. Classic textbook solutions perform
poorly when the dimension of the data is of a magnitude similar to the sample
size, or even larger. In such settings, there is a common remedy for both
statistical problems: nonlinear shrinkage of the eigenvalues of the sample
covariance matrix. The optimal nonlinear shrinkage formula depends on unknown
population quantities and is thus not available. It is, however, possible to
consistently estimate an oracle nonlinear shrinkage, which is motivated on
asymptotic grounds. A key tool to this end is consistent estimation of the set
of eigenvalues of the population covariance matrix (also known as the
spectrum), an interesting and challenging problem in its own right. Extensive
Monte Carlo simulations demonstrate that our methods have desirable
finite-sample properties and outperform previous proposals.Comment: 40 pages, 8 figures, 5 tables, University of Zurich, Department of
Economics, Working Paper No. 105, Revised version, July 201