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 (PCA) 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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Bouroche, J.-M., & Saporta, G. (1980). L’analyse des données. Paris: Presses Universitaires de France.
Fengler, M. R., Härdle, W., & Villa, C. (2003). The dynamics of implied volatilities: A common principal components approach. Review of Derivative Research, 6, 179–202.
Flury, B. (1988). Common principle components analysis and related multivariate models. New York: Wiley.
Flury, B., & Gautschi, W. (1986). An algorithm for simultaneous orthogonal transformation of several positive definite symmetric matrices to nearly diagonal form. SIAM Journal on Scientific and Statistical Computing, 7, 169–184.
Muirhead, R. J. (1982). Aspects of multivariate statistics. New York: Wiley.
Volle, V. (1985). Analyse des Données. Paris: Economica.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Härdle, W.K., Simar, L. (2015). Principal Components Analysis. In: Applied Multivariate Statistical Analysis. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-45171-7_11
Download citation
DOI: https://doi.org/10.1007/978-3-662-45171-7_11
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-662-45170-0
Online ISBN: 978-3-662-45171-7
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)