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The perceived framework of a classical statistic: Is the non-invariance of a Wald statistic much ado about null thing?

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  • Dastoor, Naorayex

    ()
    (University of Alberta, Department of Economics)

Abstract

The distinction between a nominal framework for the three classical statistics and a perceived framework for each classical statistic provides more ways to interpret these statistics, and intuitively explains as well as more easily shows some well-known results. In particular, each classical statistic can be viewed in terms of a length in each of four spaces and, since the classical procedures per se are equivalent in a perceived framework, two statistics are identical if their perceived frameworks are identical. This helps to integrate the normally separately treated issues of a reformulation of a null hypothesis and of locally equivalent alternatives. For example, a Wald statistic is not invariant if a reformulation changes its perceived framework, and an appropriate score statistic is invariant as its perceived framework is unaffected by considering a locally equivalent alternative. [During the thirty-four months this paper was under consideration at The Econometrics Journal, the Editor-in-charge (Professor Stephane Gregoir) did not reply to three (of the author's four) requests about the status of the submission, and provided neither a referee's report nor a first decision. Also, when asked to intervene by the author, the new Managing Editor (Professor Richard J Smith) offered the author the possibility of submitting the paper (as a new submission) to the new editorial regime, at which point, the author withdrew the paper.]

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Bibliographic Info

Paper provided by University of Alberta, Department of Economics in its series Working Papers with number 2009-25.

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Length: 43 pages
Date of creation: 01 Aug 2009
Date of revision:
Handle: RePEc:ris:albaec:2009_025

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Keywords: classical statistic; likelihood ratio statistic; nominal framework; perceived framework; score statistic; Wald statistic;

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  1. Dagenais, Marcel G & Dufour, Jean-Marie, 1991. "Invariance, Nonlinear Models, and Asymptotic Tests," Econometrica, Econometric Society, vol. 59(6), pages 1601-15, November.
  2. Russell Davidson & James G. MacKinnon, 1984. "Implicit Alternatives and the Local Power of Test Statistics," Working Papers 556, Queen's University, Department of Economics.
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  9. Gordon Kemp, 2000. "Invariance and the Wald Test," Economics Discussion Papers 526, University of Essex, Department of Economics.
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  13. Godfrey, Leslie G, 1978. "Testing against General Autoregressive and Moving Average Error Models When the Regressors Include Lagged Dependent Variables," Econometrica, Econometric Society, vol. 46(6), pages 1293-1301, November.
  14. Phillips, Peter C B & Park, Joon Y, 1988. "On the Formulation of Wald Tests of Nonlinear Restrictions," Econometrica, Econometric Society, vol. 56(5), pages 1065-83, September.
  15. Breusch, T S, 1978. "Testing for Autocorrelation in Dynamic Linear Models," Australian Economic Papers, Wiley Blackwell, vol. 17(31), pages 334-55, December.
  16. Gourieroux, C. & Monfort, A., 1989. "A General Framework for Testing a Null Hypothesis in a “Mixed” Form," Econometric Theory, Cambridge University Press, vol. 5(01), pages 63-82, April.
  17. 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.
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