Title: Covariance matrix regularization through resampling
Authors: Kirill Dragun - VUB, UGent (Belgium) [presenting]
Kris Boudt - UGent, VUB, VUA (Belgium)
Steven Vanduffel - Vrije Universiteit Brussel (Belgium)
Abstract: Many covariance matrix estimators achieve higher reliability than the sample covariance matrix at the expense of positive semi-definiteness. A typical example is the element-wise estimation of the covariance matrix using the implied covariance from the estimated variance of a sum of two random variables. The resulting estimator can be called a pre-estimator which then needs refinement to be transformed into a positive semi-definite matrix. The most popular transformations are shrinkage and eigenvalue cleaning. We propose methods for adjustments of the covariance matrix estimates in a way to get it positive semidefinite, taking into account the distribution properties of the original estimator. While the primary goal of imposing the adjustment is to achieve positive semidefiniteness substantial accuracy gains are observed too.