Principal component analysis in an asymmetric norm

Arbeitspapier

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.

Angaben zum Objekt

• Sprache: Englisch

Verweise und Beziehungen

• Erschienen in: Series: SFB 649 Discussion Paper ; No. 2016-040

Klassifikation und Themen

• Klassifikation: Wirtschaft ; Multiple or Simultaneous Equation Models: Classification Methods; Cluster Analysis; Principal Components; Factor Models ; Large Data Sets: Modeling and Analysis ; Optimization Techniques; Programming Models; Dynamic Analysis ; Computational Techniques; Simulation Modeling ; Criteria for Decision-Making under Risk and Uncertainty
• Thema: principal components ; asymmetric norm ; dimension reduction ; quantile ; expectile ; fMRI ; risk attitude ; brain imaging ; temperature ; functional data

Beteiligte, Orts- und Zeitangaben

• Ereignis: Geistige Schöpfung
• (wer): Tran, Ngoc Mai ; Burdejová, Petra ; Osipenko, Maria ; Härdle, Wolfgang Karl
• Ereignis: Veröffentlichung
• (wer): Humboldt University of Berlin, Collaborative Research Center 649 - Economic Risk
• (wo): Berlin
• (wann): 2016

Weitere Informationen

• Handle: http://hdl.handle.net/10419/148876
• Letzte Aktualisierung: 10.03.2025, 11:42 MEZ