IDEAS home Printed from
   My bibliography  Save this paper

Invariance, Nonlinear Models and Asymptotic Tests


  • Dagenais, M.G.
  • Dufour, J.M.


Several 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.

Suggested Citation

  • Dagenais, M.G. & Dufour, J.M., 1987. "Invariance, Nonlinear Models and Asymptotic Tests," Cahiers de recherche 8738, Universite de Montreal, Departement de sciences economiques.
  • Handle: RePEc:mtl:montde:8738

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below 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.

    Other versions of this item:

    More about this item


    Testing ; Models;


    Access and download statistics


    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:mtl:montde:8738. 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: (Sharon BREWER). General contact details of provider: .

    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.

    We have no references for this item. You can help adding them by using 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 RePEc Author Service 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.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.