標題: 針對均值-方差最佳化的巨大共變異反矩陣估計
Estimation of Large Precision Matrix for High Dimensional Mean-Variance Optimization
作者: 匡顯吉
王秀瑛
銀慶剛
Kuang, Hsien-Chi
Wang, Hsiu-Ying
Ing, Ching-Kang
統計學研究所
關鍵字: 因子分析;共變異反矩陣;modified Cholesky decomposition;Orthogonal greedy algorithm、;均值-方差最佳解;Factor analysis;Precision matrix;Modified Cholesky decomposition;Orthogonal greedy algorithm;Mean-variance optimization
公開日期: 2016
摘要: 近幾年來透過因子分析(factor analysis)來估計高維度下的共變異矩陣(high dimensional covariance matrix)是越來越受歡迎,但要應用因子分析來估計在高維度下的共變異矩陣的反矩陣(high dimensional precision matrix)是非常的困難,因為在估計高維度誤差的共變異矩陣的反矩陣(high dimensional error precision matrix)當中,通常都含有稀疏(sparse)的限制。這篇論文結合了 modified Cholesky decomposition 以及 orthogonal greedy algorithm (OGA)的方法來估計在稀疏限制下高維度誤差的共變異矩陣的反矩陣,並應用在財務上 mean-variance portfolio optimization 的問題。在模擬的結果中,我們所提的方法比傳統的 threshold 來的更好。
Recently, it has drawn attention on estimation of high-dimensional covariance matrices by using factor analysis. However, it is very difficult to apply factor analysis estimation of high-dimensional precision matrices. Because one of the commonly used conditions for estimating high-dimensional error precision matrix is to assume the covariance matrix to be sparse. This study combine modified Cholesky decomposition and orthogonal greedy algorithm (OGA) approaches to estimate the high-dimensional precision matrix under the constraint that the covariance matrix is sparse. The result can be used to deal with the mean-variance portfolio optimization problem. According to the simulation results, the proposed approach outperforms the adaptive thresholding method.
URI: http://etd.lib.nctu.edu.tw/cdrfb3/record/nctu/#GT070352615
http://hdl.handle.net/11536/138509
顯示於類別:畢業論文