Arbeitspapier
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 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.
- Sprache
-
Englisch
- Erschienen in
-
Series: Working Paper ; No. 105
- Klassifikation
-
Wirtschaft
Estimation: General
- Thema
-
large-dimensional asymptotics
covariance matrix eigenvalues
nonlinear shrinkage
principal component analysis
Multivariate Analyse
Varianzanalyse
Theorie
- Ereignis
-
Geistige Schöpfung
- (wer)
-
Ledoit, Olivier
Wolf, Michael
- Ereignis
-
Veröffentlichung
- (wer)
-
University of Zurich, Department of Economics
- (wo)
-
Zurich
- (wann)
-
2013
- DOI
-
doi:10.5167/uzh-70168
- Handle
- Letzte Aktualisierung
-
10.03.2025, 11:44 MEZ
Datenpartner
ZBW - Deutsche Zentralbibliothek für Wirtschaftswissenschaften - Leibniz-Informationszentrum Wirtschaft. Bei Fragen zum Objekt wenden Sie sich bitte an den Datenpartner.
Objekttyp
- Arbeitspapier
Beteiligte
- Ledoit, Olivier
- Wolf, Michael
- University of Zurich, Department of Economics
Entstanden
- 2013
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