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Principal Components Analysis

  • Wolfgang Karl HärdleEmail author
  • Léopold Simar
Chapter

Abstract

Chapter 10 presented the basic geometric tools needed to produce a lower dimensional description of the rows and columns of a multivariate data matrix. Principal components analysis has the same objective with the exception that the rows of the data matrix \({{\mathcal {X}}}\) will now be considered as observations from a p-variate random variable X. The principle idea of reducing the dimension of X is achieved through linear combinations.

References

  1. J.-M. Bouroche, Saporta, G., L’analyse des données(Presses Universitaires de France, Paris, 1980)Google Scholar
  2. M.R. Fengler, W. Härdle, C. Villa, The dynamics of implied volatilities: a common principal components approach. Rev. Deriv. Res. 6, 179–202 (2003)CrossRefGoogle Scholar
  3. B. Flury, Common Principle Components Analysis and Related Multivariate Models (Wiley, New York, 1988)Google Scholar
  4. B. Flury, W. Gautschi, An Algorithm for simultaneous orthogonal transformation of several positive definite symmetric matrices to nearly diagonal form. SIAM J. Sci. Stat. Comput. 7, 169–184 (1986)MathSciNetCrossRefGoogle Scholar
  5. R.J. Muirhead, Aspects of Multivariate Statistics (Wiley, New York, 1982)Google Scholar
  6. V. Volle, Analyse des Données (Economica, Paris, 1985)Google Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Ladislaus von Bortkiewicz Chair of StatisticsHumboldt-Universität zu BerlinBerlinGermany
  2. 2.Institute of Statistics, Biostatistics and Actuarial SciencesUniversité Catholique de LouvainLouvain-la-NeuveBelgium

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