Title: Factor model estimation by composite minimization
Authors: Matteo Farne - University of Bologna (Italy) [presenting]
Abstract: The problem of factor model estimation in large dimensions is addressed under the low rank plus sparse assumption. Existing approaches based on PCA like POET estimator fail to catch low rank spaces characterized by non-spiked eigenvalues, as in this case the asymptotic consistency of PCA defaults. UNLOREC, an alternative approach based on the minimization of a low rank plus sparse decomposition problem, is shown to produce the covariance estimate with the least possible dispersed eigenvalues among all the matrices having the same rank of the low rank component and the same support of the sparse component. Consequently, if dimension and sample size are fixed, loadings and factor scores estimated via UNLOREC provide the tightest possible error bound. The result is based on the eigenvalue dispersion lemma. The effectiveness of UNLOREC factor estimates is finally explored in an exhaustive simulation study, which clarifies that the gain of UNLOREC is larger as the latent eigenvalues are less spiked and the sparse component is more sparse.