Not logged in.
Quick Search - Contribution
Contribution Details
Type | Working Paper |
Scope | Discipline-based scholarship |
Title | Shrinkage estimation of large covariance matrices: keep it simple, statistician? |
Organization Unit | |
Authors |
|
Language |
|
Institution | University of Zurich |
Series Name | Working paper series / Department of Economics |
Number | 327 |
ISSN | 1664-705X |
Number of Pages | 34 |
Date | 2021 |
Abstract Text | Under rotation-equivariant decision theory, sample covariance matrix eigenvalues can be optimally shrunk by recombining sample eigenvectors with a (potentially nonlinear) function of the unobservable population covariance matrix. The optimal shape of this function reflects the loss/risk that is to be minimized. We solve the problem of optimal covariance matrix estimation under a variety of loss functions motivated by statistical precedent, probability theory, and differential geometry. A key ingredient of our nonlinear shrinkage methodology is a new estimator of the angle between sample and population eigenvectors, without making strong assumptions on the population eigenvalues. We also introduce a broad family of covariance matrix estimators that can handle all regular functional transformations of the population covariance matrix under large-dimensional asymptotics. In addition, we compare via Monte Carlo simulations our methodology to two simpler ones from the literature, linear shrinkage and shrinkage based on the spiked covariance model. |
Other Identification Number | merlin-id:18370 |
PDF File | Download from ZORA |
Export |
BibTeX
EP3 XML (ZORA) |
Keywords | Large-dimensional asymptotics, random matrix theory, rotation equivariance, Kovarianzfunktion, Risikomanagement, Verlust, Modellierung, Eigenwert, Monte-Carlo-Simulation |
Additional Information | Revised version |