2 research outputs found
A calibration method for non-positive definite covariance matrix in multivariate data analysis
Covariance matrices that fail to be positive definite arise often in covariance estimation. Approaches addressing this problem exist, but are not well supported theoretically. In this paper, we propose a unified statistical and numerical matrix calibration, finding the optimal positive definite surrogate in the sense of Frobenius norm. The proposed algorithm can be directly applied to any estimated covariance matrix. Numerical results show that the calibrated matrix is typically closer to the true covariance, while making only limited changes to the original covariance structure
A nonparametric empirical Bayes approach to covariance matrix estimation
We propose an empirical Bayes method to estimate high-dimensional covariance
matrices. Our procedure centers on vectorizing the covariance matrix and
treating matrix estimation as a vector estimation problem. Drawing from the
compound decision theory literature, we introduce a new class of decision rules
that generalizes several existing procedures. We then use a nonparametric
empirical Bayes g-modeling approach to estimate the oracle optimal rule in that
class. This allows us to let the data itself determine how best to shrink the
estimator, rather than shrinking in a pre-determined direction such as toward a
diagonal matrix. Simulation results and a gene expression network analysis
shows that our approach can outperform a number of state-of-the-art proposals
in a wide range of settings, sometimes substantially.Comment: 20 pages, 4 figure