Principal component analysis in an asymmetric norm

Ngoc Mai Tran, Petra Burdejová, Maria Osipenko and Wolfgang Härdle

No 2016-040, SFB 649 Discussion Papers from Humboldt University Berlin, Collaborative Research Center 649: Economic Risk

Abstract: Principal component analysis (PCA) is a widely used dimension reduction tool in the analysis of high-dimensional data. However, in many applications such as risk quantification in finance or climatology, one is interested in capturing the tail variations rather than variation around the mean. In this paper, 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 one approximates uctuations in the expectile level of the data by a low dimensional subspace. We provide algorithms based on iterative least squares, prove upper bounds on their convergence times, and compare their performances in a simulation study. We apply the algorithms to a Chinese weather dataset and fMRI data from an investment decision study.

Keywords: principal components; asymmetric norm; dimension reduction; quantile; expectile; fMRI; risk attitude; brain imaging; temperature; functional data (search for similar items in EconPapers)
JEL-codes: C38 C55 C61 C63 D81 (search for similar items in EconPapers)
Date: 2016
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Related works:
Journal Article: Principal component analysis in an asymmetric norm (2019)
Working Paper: Principal component analysis in an asymmetric norm (2014)
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