IDEAS home Printed from
MyIDEAS: Log in (now much improved!) to save this paper

The Geometry of the Wald Test

Listed author(s):
  • Russell Davidson

The issue of the non-invariance of the Wald test under nonlinear reparametrisations of the restrictions under test is studied from a differential geometric viewpoint. Quantities that can be defined in purely geometrical terms are by construction invariant under reparametrisation, and various attempts are made to construct a Wald test out of such invariant quantities only. Despite the existence of a wide variety of possibilities, no computationally convenient invariant test statistic emerges from the analysis, since all the statistics considered need calculations equivalent in difficulty to the estimation of the restricted model, contrary to the spirit of the Wald test. On the other hand a variant of a C(alpha) test is discussed which, while not completely invariant under reparametrisation, is very nearly so, at least in the context of the model discussed by Gregory and Veall (1985), for which the conventional Wald test is particularly badly behaved. This test is easily computed from estimates of the unrestricted model only, and Monte Carlo evidence supports the conclusion that it yields as reliable inference as any other classical test even in very small samples.

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:
File Function: First version 2013
Download Restriction: no

Paper provided by Queen's University, Department of Economics in its series Working Papers with number 800.

in new window

Date of creation: Jan 1990
Handle: RePEc:qed:wpaper:800
Contact details of provider: Postal:
Kingston, Ontario, K7L 3N6

Phone: (613) 533-2250
Fax: (613) 533-6668
Web page:

More information through EDIRC

No references listed on IDEAS
You can help add them by filling out this form.

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

When requesting a correction, please mention this item's handle: RePEc:qed:wpaper:800. 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: (Mark Babcock)

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.

This information is provided to you by IDEAS at the Research Division of the Federal Reserve Bank of St. Louis using RePEc data.