Covariance matrix filtering with bootstrapped hierarchies

Abstract

Statistical inference of the dependence between objects often relies on covariance matrices. Unless the number of features (e.g. data points) is much larger than the number of objects, covariance matrix cleaning is necessary to reduce estimation noise. We propose a method that is robust yet flexible enough to account for fine details of the structure covariance matrix. Robustness comes from using a hierarchical ansatz and dependence averaging between clusters; flexibility comes from a bootstrap procedure. This method finds several possible hierarchical structures in DNA microarray gene expression data, and leads to lower realized risk in global minimum variance portfolios than current filtering methods when the number of data points is relatively small.

10 pages, 9 figures

References in corpus (5)

• Nonlinear shrinkage estimation of large-dimensional covariance matrices
• Cleaning large correlation matrices: tools from random matrix theory
• Spanning Trees and bootstrap reliability estimation in correlation based networks
• Nonparametric sign prediction of high-dimensional correlation matrix coefficients
• Cross-validation based Nonlinear Shrinkage

Cited by in corpus (4)

• Nonparametric sign prediction of high-dimensional correlation matrix coefficients
• Two-step estimators of high dimensional correlation matrices
• End-to-End Large Portfolio Optimization for Variance Minimization with Neural Networks through Covariance Cleaning
• Quantifying the information lost in optimal covariance matrix cleaning