Tobias Rydén: Data-driven rotation invariant shrinkage of covariance matrices with splines

Abstract

We propose a data-driven approach to rotation invariant estimation of (large inverse) covariance matrices. Such estimators take a preliminary estimator, often the sample covariance matrix, and modify its eigenvalues. The proposed method models the function mapping preliminary eigenvalues to modified ones as a cubic spline, estimated using a variation of cross-validation. There is a considerable literature on asymptotically optimal rotation invariant estimators, but the proposed idea gives more flexibility in the choice a suitable loss function, the choice of preliminary estimator, and, potentially, allowing for dependent data. A small numerical example illustrates that the approach can beat linear shrinkage for a variety of loss functions and, depending on the loss function, beat or be on par with asymptotically optimal estimators.

Zoom id
In order to obtain a zoom link please register by sending an email to Dmitry Otryakhin at otryakhin@math.su.se .