A1118
Title: Well-conditioned covariance estimation via Bayesian eigenvalue regularization
Authors: Jesper Cremers - Vrije Universiteit Brussel (VUB) (Belgium) [presenting]
Kris Boudt - Vrije Universiteit Brussel and VU Amsterdam (Belgium)
Steven Vanduffel - Vrije Universiteit Brussel (Belgium)
Kirill Dragun - VUB, UGent (Belgium)
Abstract: Covariance matrices and their inverses are fundamental to a wide range of statistical applications. Traditional estimators often produce ill-conditioned or (nearly) singular matrices due to the presence of over-dispersed eigenvalues. We propose an explicit approach to regularize the eigenvalues of a class of covariance estimators using Bayes' theorem and a flexible prior that enforces positive semidefiniteness. A data-driven procedure determines the intensity of regularization, under which insights can be made into its behavior. The resulting estimators are both well-conditioned and accurate with respect to predictive performance. In a simulation study, we show that our proposed framework outperforms alternative rotation-invariant estimators. We validate its practical relevance through an empirical application to minimum-variance portfolios. Our approach significantly reduces out-of-sample variance and portfolio turnover.
