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Title: High-Dimensional Analysis On Matrix Decomposition With Application To Correlation Matrix Estimation In Factor Models
Authors: WU BIN
Keywords: matrix decomposition, low-rank, sparse, high-dimensional, correlation matrix, factor model
Issue Date: 24-Jan-2014
Citation: WU BIN (2014-01-24). High-Dimensional Analysis On Matrix Decomposition With Application To Correlation Matrix Estimation In Factor Models. ScholarBank@NUS Repository.
Abstract: In this thesis, we conduct high-dimensional analysis on the problem of low-rank and sparse matrix decomposition with fixed and sampled basis coefficients. This problem is strongly motivated by high-dimensional correlation matrix estimation coming from factor models used in economic and financial studies. For the noiseless version, we provide probabilistic exact recovery guarantees in the high-dimensional setting if certain identifiability conditions for the low-rank and sparse components are satisfied. For the noisy version, inspired by the successful recent development on the adaptive nuclear semi-norm penalization technique, we propose a two-stage rank-sparsity-correction procedure and examine its recovery performance by establishing a novel non-asymptotic probabilistic error bound under the high-dimensional scaling. We then specialize this two-stage correction procedure to deal with the correlation matrix estimation problem with missing observations in strict factor models. In this application, the specialized recovery error bound and the convincing numerical results validate the superiority of the proposed approach.
Appears in Collections:Ph.D Theses (Open)

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