This file is part of IDEAS, which uses RePEc data


[ Papers | Articles | Software | Books | Chapters | Authors | Institutions | JEL Classification | NEP reports | Search | New papers by email | Author registration | Rankings | Volunteers | FAQ | Blog | Help! ]

Tail Probabilities of the Maxima of Multilinear Forms and Their Applications

Author info | Abstract | Publisher info | Download info | Related research | Statistics
Author Info
Akimichi Takemura (Faculty of Economics, University of Tokyo.)
Satoshi Kuriki (The Institute of Statistical Mathematics.)
Abstract

Let Z be a k-way array whose q1 x...x qk elements are independent standard normal variables. For qi-dimensional vector hi, i=1, ...., k, define a multilinear form of degree k by (h1 x hk)'vec(Z). We derive formulas for upper tail probabilities of the maximum of multilinear form with respect to hi's under the condition ||hi||=1 for any i, and of its standardized statistic obtained by dividing by ||vec(Z)||. We also give formulas for the maximum of symmetric multilinear form (h1 x...x hk)'vec(sym(Z)),@where sym(Z) denotes the symmetrization of Z with respect to indices. These classes of statistics have important applications in testing hypotheses of multivariate analysis such as the analysis of variance of multiway layout data or testing multivariate normality. In order to derive the tail probabilities we employ a geometric approach developed by H. Weyl and J. Sun. Upper and lower bounds for the tail probabilities are given by reexamining the Sun's results. Some numerical examples are given to illustrate the practical usefulness of the obtained formulas including the upper and lower bounds.

Download Info
To download:

If you experience problems downloading a file, check if you have the proper application to view it first. Information about this may be contained in the File-Format links below. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.

File URL: http://www.e.u-tokyo.ac.jp/cirje/research/dp/98/cf4/contents.htm
File Format: text/html
File Function:
Download Restriction: no

Publisher Info
Paper provided by CIRJE, Faculty of Economics, University of Tokyo in its series CIRJE F-Series with number CIRJE-F-4.

Download reference. The following formats are available: HTML (with abstract), plain text (with abstract), BibTeX, RIS (EndNote, RefMan, ProCite), ReDIF
Length: 40 pages
Date of creation: Jun 1998
Date of revision:
Handle: RePEc:tky:fseres:98cf04

Contact details of provider:
Web page: http://www.e.u-tokyo.ac.jp/cirje/index.htm

For technical questions regarding this item, or to correct its listing, contact: ().

Related research
Keywords:

Other versions of this item:

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Davis, A. W., 1972. "On the ratios of the individual latent roots to the trace of a Wishart matrix," Journal of Multivariate Analysis, Elsevier, vol. 2(4), pages 440-443, December. [Downloadable!] (restricted)
Full references

Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Akimichi Takemura & Satoshi Kuriki, 1999. "Tail Probability via Tube Formula and Euler Characteristic Method when Critical Radius is Zero," CIRJE F-Series CIRJE-F-59, CIRJE, Faculty of Economics, University of Tokyo. [Downloadable!]
  2. Akimichi Takemura & Satoshi Kuriki, 1999. "Maximum of Gaussian Field on Piecewise Smooth Domain: Equivalence of Tube Method and Euler Characteristic Method," CIRJE F-Series CIRJE-F-54, CIRJE, Faculty of Economics, University of Tokyo. [Downloadable!]
  3. Akimichi Takemura & Satoshi Kuriki, 2000. "Maximum Covariance Di erence Test for Equality of Two Covariance Matrices," CIRJE F-Series CIRJE-F-89, CIRJE, Faculty of Economics, University of Tokyo. [Downloadable!]
Statistics
Access and download statistics

Did you know? The yearly budget of IDEAS is exactly $0: it relies entirely on volunteer work.

This page was last updated on 2009-12-3.

This information is provided to you by IDEAS at the Department of Economics, College of Liberal Arts and Sciences, University of Connecticut using RePEc data on a server sponsored by the Society for Economic Dynamics.