NOVELIST Estimator of Large Correlation and Covariance Matrices and Their Inverses

• Activity Number: 650
• Type: Contributed
• Date/Time: Thursday, August 13, 2015 : 8:30 AM to 10:20 AM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Na Huang* and Piotr Fryzlewicz
• Companies: London School of Economics and London School of Economics
• Keywords: covariance regularisation ; high-dimensional covariance ; long memory ; non-sparse modelling ; singular sample covariance ; high dimensionality

Abstract

We propose a "NOVEL Integration of the Sample and Thresholded covariance estimators" (NOVELIST) to estimate the large covariance (correlation) and precision matrix. NOVELIST performs shrinkage of the sample covariance (correlation) towards its thresholded version. The sample covariance (correlation) component is non-sparse and can be low-rank in high dimensions. The thresholded sample covariance (correlation) component is sparse, and its addition ensures the stable invertibility of NOVELIST. The benefits of the NOVELIST estimator include simplicity, ease of implementation, computational efficiency and the fact that its application avoids eigenanalysis. We obtain an explicit convergence rate in the operator norm over a large class of covariance (correlation) matrices when the dimension $p$ and the sample size $n$ satisfy log $p/n\to 0$. In empirical comparisons with several popular estimators, the NOVELIST estimator in which the amount of shrinkage and thresholding is chosen by cross-validation performs well in estimating covariance and precision matrices over a wide range of models and sparsity classes.