Title. Multi Anchor Point Shrinkage for the Covariance Matrix Estimation

Abstract. In financial equity data sets, estimation of a high-dimensional covariance matrix is well-known to be impeded by the lack of a long data history. To address this problem, shrinkage estimators for the leading eigenvector (1st PC) of a sample covariance matrix have recently been developed. These estimators are particularly suited to high-dimensional and low sample-size problems but are not consistent. We introduce a more general framework -- multi-anchor point shrinkage (MAPS) -- which provably yields consistent estimators when supplied with mild ordering information. Such results were previously thought to be possible only when the sample size grew with the dimension. We further analyze the properties of the MAPS estimator when the ordering information is not available and discuss how this information may be inferred from equity data sets. Finally, we numerically illustrate the performance of the estimator on an application in portfolio theory.

Bio: Hubeyb Gurdogan holds Master's degrees in pure mathematics from Bilkent University and Syracuse University. He obtained his PhD in Mathematics in 2021 from Florida State University under the supervision of Prof. Alec Kercheval. Hubeyb is currently a Postdoctoral Scholar at the Consortium for Data Analytics in Risk (CDAR) at UC Berkeley. His primary research interests include stochastic analysis, high dimensional statistics, and neural networks with an emphasis on mathematical finance.