Advanced Search
MyIDEAS: Login to save this paper or follow this series

Fractional Matrix Calculus and the Distribution of Multivariate Tests

Contents:

Author Info

Abstract

Fractional matrix operator methods are introduced as a new tool of distribution theory for use in multivariate analysis and econometrics. Earlier work by the author on this operational calculus is reviewed and to illustrate the use of these methods we give an exact distribution theory for a general class of tests in the multivariate linear model. This distribution theory unifies and generalizes previously known results, including those for the standard F statistic in linear regression, for Hotelling's T^{2} test and for Hotelling's generalized T^{-2} test. We also provide a simple and novel derivation of conventional asymptotic theory as a specialization of exact theory. This approach is extended to generate general formulae for higher order asymptotic expansions. Thus, the results of the paper provide a meaningful unification of conventional asymptotics, higher order asymptotic expansions and exact finite sample distribution theory in this context.

Download Info

If you experience problems downloading a file, check if you have the proper application to view it first. 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://cowles.econ.yale.edu/P/cd/d07b/d0767.pdf
Download Restriction: no

Bibliographic Info

Paper provided by Cowles Foundation for Research in Economics, Yale University in its series Cowles Foundation Discussion Papers with number 767.

as in new window
Length: 23 pages
Date of creation: Sep 1985
Date of revision:
Publication status: Published in I.B. MacNeill and G.J. Umphrey, eds., Time Series and Econometric Modelling, Reidel, 1987, pp. 219-234
Handle: RePEc:cwl:cwldpp:767

Note: CFP 664.
Contact details of provider:
Postal: Yale University, Box 208281, New Haven, CT 06520-8281 USA
Phone: (203) 432-3702
Fax: (203) 432-6167
Web page: http://cowles.econ.yale.edu/
More information through EDIRC

Order Information:
Postal: Cowles Foundation, Yale University, Box 208281, New Haven, CT 06520-8281 USA

Related research

Keywords: Fractional matrix calculus; multivariate tests; exact distribution theory; asymptotic expansions;

References

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.:
as in new window
  1. Peter C.B. Phillips, 1983. "The Exact Distribution of the Stein-Rule Estimator," Cowles Foundation Discussion Papers 682, Cowles Foundation for Research in Economics, Yale University.
  2. Knight, John. L., 1986. "The Distribution of the Stein-Rule Estimator in a Model with Non-Normal Disturbances," Econometric Theory, Cambridge University Press, vol. 2(02), pages 202-219, August.
  3. Peter C.B. Phillips, 1983. "Finite Sample Econometrics Using ERA's," Cowles Foundation Discussion Papers 683, Cowles Foundation for Research in Economics, Yale University.
  4. Peter C.B. Phillips, 1984. "The Exact Distribution of the Wald Statistic," Cowles Foundation Discussion Papers 722, Cowles Foundation for Research in Economics, Yale University.
  5. Peter C.B. Phillips, 1983. "An Everywhere Convergent Series Representation of the Distribution of Hotelling's Generalized T_{0}^{2}," Cowles Foundation Discussion Papers 723R, Cowles Foundation for Research in Economics, Yale University, revised Mar 1986.
  6. Phillips, Peter C B, 1985. "The Exact Distribution of the SUR Estimator," Econometrica, Econometric Society, vol. 53(4), pages 745-56, July.
Full references (including those not matched with items on IDEAS)

Citations

Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
as in new window

Cited by:
  1. Peter C.B. Phillips, 1992. "Some Exact Distribution Theory for Maximum Likelihood Estimators of Cointegrating Coefficients in Error Correction Models," Cowles Foundation Discussion Papers 1039, Cowles Foundation for Research in Economics, Yale University.
  2. Peter C.B. Phillips, 1999. "Discrete Fourier Transforms of Fractional Processes," Cowles Foundation Discussion Papers 1243, Cowles Foundation for Research in Economics, Yale University.

Lists

This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

Statistics

Access and download statistics

Corrections

When requesting a correction, please mention this item's handle: RePEc:cwl:cwldpp:767. See general information about how to correct material in RePEc.

For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Glena Ames).

If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

If references are entirely missing, you can add them using this form.

If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.

If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.

Please note that corrections may take a couple of weeks to filter through the various RePEc services.