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Internal Seminars 2017: Factor model estimation by composite minimization

08/06/2017 dalle 13:15 alle 14:35

Dove Dipartimento di Scienze Statistiche, via delle Belle Arti n. 41 - Aula III 2° piano

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Matteo Farné
Research fellow, Dipartimento di Scienze Statistiche - Bologna


In this talk, we address the problem of factor model estimation in large dimensions under the low rank plus sparse assumption. Existing approaches based on PCA (POET, Fan et al. 2013), fail to catch low rank spaces characterized by non-spiked eigenvalues, as in this case the asymptotic consistency of PCA established in (Bai, 2003) defaults. UNLOREC, an alternative approach based on the minimization of a low rank plus sparse decomposition problem, has been developed in (Luo, 2013) and (Farnè, 2016). This method 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. As a consequence, 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 in (Ledoit and Wolf, 2004). The effectiveness of UNLOREC factor estimates is finally explored in an exhaustive simulation study, which clarifies the advantages of UNLOREC.

Alessandra Luati, Silvia Cagnone