10. Principal Component Analysis

  1. Yasunori Fujikoshi1,
  2. Vladimir V. Ulyanov2 and
  3. Ryoichi Shimizu3

Published Online: 22 AUG 2011

DOI: 10.1002/9780470539873.ch10

Multivariate Statistics: High-Dimensional and Large-Sample Approximations

Multivariate Statistics: High-Dimensional and Large-Sample Approximations

How to Cite

Fujikoshi, Y., Ulyanov, V. V. and Shimizu, R. (2010) Principal Component Analysis, in Multivariate Statistics: High-Dimensional and Large-Sample Approximations, John Wiley & Sons, Inc., Hoboken, NJ, USA. doi: 10.1002/9780470539873.ch10

Author Information

  1. 1

    Chuo University, Tokyo, Japan

  2. 2

    Moscow State University, Moscow, Russia

  3. 3

    Institute of Statistical Mathematics, Tokyo, Japan

Publication History

  1. Published Online: 22 AUG 2011
  2. Published Print: 6 JAN 2010

ISBN Information

Print ISBN: 9780470411698

Online ISBN: 9780470539873

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Keywords:

  • principal components;
  • characteristic roots;
  • Wishart distribution;
  • covariance structures;
  • fixed-effect principal component model

Summary

This chapter contains sections titled:

  • Definition of Principal Components

  • Optimality of Principal Components

  • Sample Principal Components

  • MLEs of the Characteristic Roots and Vectors

  • Distributions of the Characteristic Roots

  • Model Selection Approach for Covariance Structures

  • Methods Related to Principal Components