5. Asymptotic Expansions for Multivariate Basic Statistics

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

Published Online: 22 AUG 2011

DOI: 10.1002/9780470539873.ch5

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) Asymptotic Expansions for Multivariate Basic Statistics, in Multivariate Statistics: High-Dimensional and Large-Sample Approximations, John Wiley & Sons, Inc., Hoboken, NJ, USA. doi: 10.1002/9780470539873.ch5

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:

  • Edgeworth expansion;
  • sample mean vector;
  • covariance matrix;
  • asymptotic expansions;
  • perturbation method

Summary

This chapter contains sections titled:

  • Edgeworth Expansion and its Validity

  • Sample Mean Vector and Covariance Matrix

  • T2 Statistic

  • Statistics with a Class of Moments

  • Perturbation Method

  • Cornish–Fisher Expansions

  • Transformations for Improved Approximations

  • Bootstrap Approximations

  • High-Dimensional Approximations