B1135
Title: Estimating large covariance matrices via low rank plus sparse decomposition
Authors: Matteo Farne - University of Bologna (Italy) [presenting]
Abstract: A large dimensional covariance matrix estimation method under the approximate factor model assumptions is presented. Existing methods perform estimation by extracting principal components and then applying a soft thresholding algorithm. In the described method, the low rank plus sparse decomposition for the covariance matrix is recovered by least squares minimization under nuclear norm plus $l_1$ norm penalization. The non-smooth convex minimization procedure is based on subdifferential methods, and results in a singular value thresholding plus a soft thresholding algorithm. Non asymptotic error rates can be derived under different theoretical assumptions on the eigenvalues and the sparsity pattern of $\Sigma$. It is possible to show that the unshrinkage of the estimated eigenvalues improves the performance of our estimator considerably. An ad-hoc model selection criterion which detects the optimal point in terms of composite penalty is proposed. A wide simulation study where various low rank plus sparse settings are simulated according to different parameter values is described and the improvements upon existing methods are outlined in detail.
