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Principles and Methods in the Testing of Alternative Models


  • Fisher, Gordon
  • McAleer, Michael


This paper seeks to distinguish the principles upon which testing of statistical hypotheses may be based and the practical methods which these principles generate. Six examples are given for the case of nested hypotheses as illustrations. In particular, Seber's (1964) conclusion that the Wald, Lagrange Multiplier and Likelihood Ratio Principles all lead to exactly the same test statistic in the case of a linear hypothesis, is re-examined in the light of a strict interpretation of these principles. Simple relations between various test statistics and their distributions are outlined. The concept of an artificial model is analyzed. A distinction is made between an artificial model that is in some sense an 'unrestricted' specification and one that is simply an algorithm. For non-nested hypotheses, an artificial model with prior information on the parameters is regarded as conforming to the Wald Principle. When arbitrary numerical methods are used as 'identifying' restrictions, the artificial model reduces to an algorithm since it cannot reasonably be 'accepted'.

Suggested Citation

  • Fisher, Gordon & McAleer, Michael, 1980. "Principles and Methods in the Testing of Alternative Models," Queen's Institute for Economic Research Discussion Papers 275167, Queen's University - Department of Economics.
  • Handle: RePEc:ags:queddp:275167
    DOI: 10.22004/ag.econ.275167

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    References listed on IDEAS

    1. Pesaran, M H & Deaton, Angus S, 1978. "Testing Non-Nested Nonlinear Regression Models," Econometrica, Econometric Society, vol. 46(3), pages 677-694, May.
    2. Davidson, Russell & MacKinnon, James G, 1981. "Several Tests for Model Specification in the Presence of Alternative Hypotheses," Econometrica, Econometric Society, vol. 49(3), pages 781-793, May.
    3. M. H. Pesaran, 1974. "On the General Problem of Model Selection," Review of Economic Studies, Oxford University Press, vol. 41(2), pages 153-171.
    4. Kloek, T, 1975. "Note on a Large-Sample Result in Specification Analysis," Econometrica, Econometric Society, vol. 43(5-6), pages 933-936, Sept.-Nov.
    5. T. S. Breusch & A. R. Pagan, 1980. "The Lagrange Multiplier Test and its Applications to Model Specification in Econometrics," Review of Economic Studies, Oxford University Press, vol. 47(1), pages 239-253.
    6. Hausman, Jerry, 2015. "Specification tests in econometrics," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 38(2), pages 112-134.
    7. Giles, D E A & Smith, R G, 1977. "A Note on the Minimum Error Variance Rule and the Restricted Regression Model," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 18(1), pages 247-251, February.
    8. Quandt, Richard E, 1974. "A Comparison of Methods for Testing Nonnested Hypotheses," The Review of Economics and Statistics, MIT Press, vol. 56(1), pages 92-99, February.
    9. Morgan, Alison & Vandaele, Waiter, 1974. "On testing hypothesis in simultaneous equation models," Journal of Econometrics, Elsevier, vol. 2(1), pages 55-65, May.
    10. McAleer, Michael, 1980. "The minimum error variance rule for non-linear regression models," Economics Letters, Elsevier, vol. 6(1), pages 17-21.
    11. Schmidt, Peter, 1974. "A Note on Theil's Minimum Standard Error Criterion when the Disturbances are Autocorrelated," The Review of Economics and Statistics, MIT Press, vol. 56(1), pages 122-123, February.
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    Cited by:

    1. Gordon Fisher & Allan W. Gregory & Michael McAleer, 1980. "Two Papers on Linear Models," Working Paper 411, Economics Department, Queen's University.

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