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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. Gordon Kemp, 2000. "Invariance and the Wald Test," Economics Discussion Papers 526, University of Essex, Department of Economics.
  2. Dale J. Poirier, 1995. "Intermediate Statistics and Econometrics: A Comparative Approach," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262161494, January.
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  11. 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.
  12. Breusch, T S & Pagan, A R, 1979. "A Simple Test for Heteroscedasticity and Random Coefficient Variation," Econometrica, Econometric Society, vol. 47(5), pages 1287-94, September.
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  14. Lafontaine, Francine & White, Kenneth J., 1986. "Obtaining any Wald statistic you want," Economics Letters, Elsevier, vol. 21(1), pages 35-40.
  15. Mizon, Grayham E & Richard, Jean-Francois, 1986. "The Encompassing Principle and Its Application to Testing Non-nested Hypotheses," Econometrica, Econometric Society, vol. 54(3), pages 657-78, May.
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