Please use this identifier to cite or link to this item: http://scholarbank.nus.edu.sg/handle/10635/53643
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
Source: 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.
URI: http://scholarbank.nus.edu.sg/handle/10635/53643
Appears in Collections:Ph.D Theses (Open)

Show full item record
Files in This Item:
File Description SizeFormatAccess SettingsVersion 
WuBin.pdf1.1 MBAdobe PDF

OPEN

NoneView/Download

Page view(s)

199
checked on Dec 11, 2017

Download(s)

207
checked on Dec 11, 2017

Google ScholarTM

Check


Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.