Principal component analysis in an asymmetric norm

JOURNAL OF MULTIVARIATE ANALYSIS

卷:171

Article

Tran, Ngoc M.^1,2  Burdejova, Petra³  Ospienko, Maria³  Haerdle, Wolfgang K.^3,4 

[1] Univ Texas Austin, Dept Math, Austin, TX 78712 USA

[2] Univ Bonn, Inst Appl Math, Bonn, Germany

[3] Humboldt Univ, CASE, Unter Linden 6, Berlin, Germany

[4] Singapore Management Univ, Sim Kee Boon Inst Financial Econ, 90 Stamford Rd, Singapore 178903, Singapore

关键词: Asymmetric norm;    Dimension reduction;    Expectile;    Growth data;    Quantile Risk attitude;    Temperature;   

DOI  :  10.1016/j.jmva.2018.10.004

来源: Elsevier

【 摘 要 】

Principal component analysis (PCA) is a widely used dimension reduction tool in high-dimensional data analysis. In risk quantification in finance, climatology and many other applications, however, the interest lies in capturing the tail variations rather than variation around the mean. To this end, we develop Principal Expectile Analysis (PEC), which generalizes PCA for expectiles. It can be seen as a dimension reduction tool for extreme value theory, where fluctuations in the tau-expectile level of the data are approximated by a low-dimensional subspace. We provide algorithms based on iterative least squares, derive bounds on their convergence time, and compare their performance through simulations. We apply the algorithms to a Chinese weather dataset and fMRI data from an investment decision study. (C) 2018 Published by Elsevier Inc.

【 授权许可】

Free