IDEAS home Printed from https://ideas.repec.org/a/ebl/ecbull/eb-08c10010.html
   My bibliography  Save this article

A simple explanation for the non-invariance of a Wald statistic to a reformulation of a null hypothesis

Author

Listed:
  • Naorayex K Dastoor

    (Department of Economics, University of Alberta)

Abstract

For a given null hypothesis and its reformulation, the associated Wald statistics are shown to be members of a wider family of statistics where all members are asymptotically equivalent under the null hypothesis. Therefore, the non-invariance of a Wald statistic (to a reformulation of a null hypothesis) is equivalent to using different members of the wider family and, in addition, this non-invariance implies that these members use different estimators of an appropriate variance-covariance matrix.

Suggested Citation

  • Naorayex K Dastoor, 2008. "A simple explanation for the non-invariance of a Wald statistic to a reformulation of a null hypothesis," Economics Bulletin, AccessEcon, vol. 3(62), pages 1-10.
  • Handle: RePEc:ebl:ecbull:eb-08c10010
    as

    Download full text from publisher

    File URL: http://www.accessecon.com/pubs/EB/2008/Volume3/EB-08C10010A.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Critchley, Frank & Marriott, Paul & Salmon, Mark, 1996. "On the Differential Geometry of the Wald Test with Nonlinear Restrictions," Econometrica, Econometric Society, vol. 64(5), pages 1213-1222, September.
    2. Gourieroux, C. & Monfort, A., 1989. "A General Framework for Testing a Null Hypothesis in a “Mixed” Form," Econometric Theory, Cambridge University Press, vol. 5(1), pages 63-82, April.
    3. Dagenais, Marcel G & Dufour, Jean-Marie, 1991. "Invariance, Nonlinear Models, and Asymptotic Tests," Econometrica, Econometric Society, vol. 59(6), pages 1601-1615, November.
    4. Phillips, Peter C B & Park, Joon Y, 1988. "On the Formulation of Wald Tests of Nonlinear Restrictions," Econometrica, Econometric Society, vol. 56(5), pages 1065-1083, September.
    5. Kemp, Gordon C. R., 2001. "Invariance and the Wald test," Journal of Econometrics, Elsevier, vol. 104(2), pages 209-217, September.
    6. Gregory, Allan W & Veall, Michael R, 1985. "Formulating Wald Tests of Nonlinear Restrictions," Econometrica, Econometric Society, vol. 53(6), pages 1465-1468, November.
    7. Davidson, Russell & MacKinnon, James G., 1993. "Estimation and Inference in Econometrics," OUP Catalogue, Oxford University Press, number 9780195060119.
    8. Lafontaine, Francine & White, Kenneth J., 1986. "Obtaining any Wald statistic you want," Economics Letters, Elsevier, vol. 21(1), pages 35-40.
    9. Dastoor, Naorayex K., 2003. "The equality of comparable extended families of classical-type and Hausman-type statistics," Journal of Econometrics, Elsevier, vol. 117(2), pages 313-330, December.
    10. Unknown, 1986. "Letters," Choices: The Magazine of Food, Farm, and Resource Issues, Agricultural and Applied Economics Association, vol. 1(4), pages 1-9.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Dastoor, Naorayex, 2009. "The perceived framework of a classical statistic: Is the non-invariance of a Wald statistic much ado about null thing?," Working Papers 2009-25, University of Alberta, Department of Economics.
    2. repec:ebl:ecbull:v:3:y:2008:i:62:p:1-10 is not listed on IDEAS
    3. Jean-Marie Dufour & Alain Trognon & Purevdorj Tuvaandorj, 2017. "Invariant tests based on M -estimators, estimating functions, and the generalized method of moments," Econometric Reviews, Taylor & Francis Journals, vol. 36(1-3), pages 182-204, March.
    4. Kemp, Gordon C. R., 2001. "Invariance and the Wald test," Journal of Econometrics, Elsevier, vol. 104(2), pages 209-217, September.
    5. Brown, Kenneth & Cribari-Neto, Francisco, 1992. "On Hypothesis Testing: A Selective Look at the Lagrange Multiplier, Likelihood Ratio and Wald Tests," Brazilian Review of Econometrics, Sociedade Brasileira de Econometria - SBE, vol. 12(2), November.
    6. Lung-fei Lee & Jihai Yu, 2012. "The C(α)-type gradient test for spatial dependence in spatial autoregressive models," Letters in Spatial and Resource Sciences, Springer, vol. 5(3), pages 119-135, October.
    7. Goh, Kim-Leng & King, Maxwell L., 1996. "Modified Wald tests for non-linear restrictions: A cautionary tale," Economics Letters, Elsevier, vol. 53(2), pages 133-138, November.
    8. Helen Popper, 1995. "Term premia comovement in German, Japanese, and U.S. domestic markets," Open Economies Review, Springer, vol. 6(1), pages 49-62, January.
    9. Crudu, Federico & Osorio, Felipe, 2020. "Bilinear form test statistics for extremum estimation," Economics Letters, Elsevier, vol. 187(C).
    10. Albers, C.J. & Critchley, F. & Gower, J.C., 2011. "Applications of quadratic minimisation problems in statistics," Journal of Multivariate Analysis, Elsevier, vol. 102(3), pages 714-722, March.
    11. Lu, Zeng-Hua & King, Maxwell L., 2004. "A Wald-type test of quadratic parametric restrictions," Economics Letters, Elsevier, vol. 83(3), pages 359-364, June.
    12. Stanislav Kolenikov & Kenneth A. Bollen, 2012. "Testing Negative Error Variances," Sociological Methods & Research, , vol. 41(1), pages 124-167, February.
    13. Dastoor, Naorayex K., 2003. "A score-type and a Hausman-type statistic based on nonsingular generalized inverses," Economics Letters, Elsevier, vol. 81(3), pages 395-401, December.
    14. Francisco J. Goerlich Gisbert, 1992. "Un test alternativo de la hipótesis de sustitución intertemporal del trabajo," Investigaciones Economicas, Fundación SEPI, vol. 16(2), pages 259-280, May.
    15. Peter Huber & Michael Pfaffermayr, 2010. "Testing for Conditional Convergence in Variance and Skewness: The Firm Size Distribution Revisited," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 72(5), pages 648-668, October.
    16. Alessandra Canepa & Raymond O'Brien, 2000. "The Size and Power of Bootstrap Tests for Linear Restrictions in Misspecified Cointegrating Relationships," Econometric Society World Congress 2000 Contributed Papers 1807, Econometric Society.
    17. Marcel G. Dagenais, 1992. "Pièges et limitations de l'analyse micro-économétrique," Économie et Prévision, Programme National Persée, vol. 102(1), pages 1-9.
    18. King, Maxwell L. & Zhang, Xibin & Akram, Muhammad, 2020. "Hypothesis testing based on a vector of statistics," Journal of Econometrics, Elsevier, vol. 219(2), pages 425-455.
    19. Lagomarsino, Elena, 2021. "Which nesting structure for the CES? A new selection approach based on input separability," Economic Modelling, Elsevier, vol. 102(C).
    20. Joel L. Horowitz, 1996. "Bootstrap Methods in Econometrics: Theory and Numerical Performance," Econometrics 9602009, University Library of Munich, Germany, revised 05 Mar 1996.
    21. Paul Hansen, 1997. "Inference on “earnings dynamics over the life cycle: New evidence for New Zealand”," New Zealand Economic Papers, Taylor & Francis Journals, vol. 31(2), pages 221-227.

    More about this item

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General

    Statistics

    Access and download statistics

    Corrections

    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:ebl:ecbull:eb-08c10010. See general information about how to correct material in RePEc.

    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 CitEc recognized a bibliographic reference but did not link an item in RePEc 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 RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: John P. Conley (email available below). General contact details of provider: .

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

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.