Principal component analysis in an asymmetric norm

Arbeitspapier

Principal component analysis (PCA) is a widely used dimension reduction tool in the analysis of many kind of high-dimensional data. It is used in signal processing, mechanical engineering, psychometrics, and other fields under different names. It still bears the same mathematical idea: the decomposition of variation of a high dimensional object into uncorrelated factors or components. However, in many of the above applications, one is interested in capturing the tail variables of the data rather than variation around the mean. Such applications include weather related event curves, expected shortfalls, and speeding analysis among others. These are all high dimensional tail objects which one would like to study in a PCA fashion. The tail character though requires to do the dimension reduction in an asymmetric norm rather than the classical L2-type orthogonal projection. We develop an analogue of PCA in an asymmetric norm. These norms cover both quantiles and expectiles, another tail event measure. The difficulty is that there is no natural basis, no 'principal components', to the k-dimensional subspace found. We propose two definitions of principal components and provide algorithms based on iterative least squares. We prove upper bounds on their convergence times, and compare their performances in a simulation study. We apply the algorithms to a Chinese weather dataset with a view to weather derivative pricing.

Angaben zum Objekt

• Sprache: Englisch

Verweise und Beziehungen

• Erschienen in: Series: SFB 649 Discussion Paper ; No. 2014-001

Klassifikation und Themen

• Klassifikation: Wirtschaft ; Multiple or Simultaneous Equation Models: Classification Methods; Cluster Analysis; Principal Components; Factor Models ; Optimization Techniques; Programming Models; Dynamic Analysis ; Computational Techniques; Simulation Modeling
• Thema: principal components ; asymmetric norm ; dimension reduction ; quantile ; expectile

Beteiligte, Orts- und Zeitangaben

• Ereignis: Geistige Schöpfung
• (wer): Tran, Ngoc Mai ; Osipenko, Maria ; Härdle, Wolfgang Karl
• Ereignis: Veröffentlichung
• (wer): Humboldt University of Berlin, Collaborative Research Center 649 - Economic Risk
• (wo): Berlin
• (wann): 2014

Weitere Informationen

• Handle: http://hdl.handle.net/10419/91576
• Letzte Aktualisierung: 20.09.2024, 08:23 MESZ