Invariance, Nonlinear Models and Asymptotic Tests
AbstractSeveral Asymptotic Tests Proposed in the Literature Are Shown Not to Be Invariant to Changes in Measurement Units Or, More Generally to Various Transformations Which Leave Both the Model and the Null Hypothesis Invariant. the Test Involved Include the Wald Test, a Variant of the Lagrange Multiplier Test, Neyman's 'C' Test, Durbin's Procedure (1970), Hausman-Type Tests and a Number of Tests Suggested by White (1982). for All These Procedures, Simply Changing Measurement Units in a Way That Leaves Both the Form of the Model and the Null Hypothesis Invariant Can Lead to Vastly Different Answers. This Problem Is Illustrated by Considering Regression Models with Box-Cox Transformations on the Variables. We Observe, in Particular, That Various Consistent Estimators of the Information Matrix Lead to Test Procedures with Different Invariance Properties. We Then Establish General Sufficient Conditions Which Ensure That Neyman's Test Is Invariant to Transformations Which Leave Invariant the Form of the Model Further, We Give Conditions Under Which a Generalized 'C' Test Applicable to General Restrictions, Is Invariant to the Algebraic Formulation of the Restrictions. in Many Practical Cases Where Wald-Type Tests Lack Invariance, We Find That a Modification of the 'C' Test Is Invariant and Hardly More Costly to Compute Than Wald Tests. This Computational Simplicity Stands in Contrast with Other Invariant Tests Such As the Likelihood Ratio Test. We Conclude That Non-Invariant Asymptotic Tests Should Be Avoided Or Used with Great Care. Further in Many Situations, the Suggested Modification of the 'C' Test Yields an Attractive Substitute to the Wald Test and to Other Invariant Tests.
Download InfoTo our knowledge, this item is not available for download. To find whether it is available, there are three options:
1. Check below under "Related research" whether another version of this item is available online.
2. Check on the provider's web page whether it is in fact available.
3. Perform a search for a similarly titled item that would be available.
Bibliographic InfoPaper provided by Universite de Montreal, Departement de sciences economiques in its series Cahiers de recherche with number 8738.
Length: 44P. pages
Date of creation: 1987
Date of revision:
Contact details of provider:
Postal: CP 6128, Succ. Centre-Ville, Montréal, Québec, H3C 3J7
Phone: (514) 343-6540
Fax: (514) 343-5831
Web page: http://www.sceco.umontreal.ca
More information through EDIRC
Testing ; Models;
Other versions of this item:
- Dagenais, Marcel G & Dufour, Jean-Marie, 1991. "Invariance, Nonlinear Models, and Asymptotic Tests," Econometrica, Econometric Society, vol. 59(6), pages 1601-15, November.
You can help add them by filling out this form.
CitEc Project, subscribe to its RSS feed for this item.
This item has more than 25 citations. To prevent cluttering this page, these citations are listed on a separate page. reading list or among the top items on IDEAS.Access and download statisticsgeneral 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: (Sharon BREWER).
If references are entirely missing, you can add them using this form.