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Reversed Score and Likelihood Ratio Tests

Author

Listed:
  • Dhaene, Geert

    (Ghent University)

  • Scaillet, Olivier

    (UNIVERSITE CATHOLIQUE DE LOUVAIN, Institut de Recherches Economiques et Sociales (IRES); UNIVERSITE CATHOLIQUE DE LOUVAIN, Institut d’Administration et de Gestion (IAG))

Abstract

Two extensions of a parametric model are proposed, each one involving the score function of an alternative parametric model. We show that the encompassing hypothesis is equivalent to standard conditions on the score of each of the extended models. The condition on the first extension gives rise to the standard score encompassing test, while the condition on the second extension induces a so-called reversed score encompassing test. A similar logic is applied to the likelihood ratio, generating a likelihood ratio and a reversed likelihood ratio encompassing test. The ensued test statistics can be based on simulations if certain calculations are too difficult to carry out analytically. We study the first order asymptotic properties of the proposed test statistics under general conditions.

Suggested Citation

  • Dhaene, Geert & Scaillet, Olivier, 2000. "Reversed Score and Likelihood Ratio Tests," LIDAM Discussion Papers IRES 2000026, Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES).
    • Handle: RePEc:ctl:louvir:2000026
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    File URL: http://sites.uclouvain.be/econ/DP/IRES/2000-26.pdf
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    References listed on IDEAS

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    1. Andrews, Donald W. K., 1987. "Asymptotic Results for Generalized Wald Tests," Econometric Theory, Cambridge University Press, vol. 3(3), pages 348-358, June.
    2. Gouriéroux, Christian & Monfort, Alain, 1995. "Testing, Encompassing, and Simulating Dynamic Econometric Models," Econometric Theory, Cambridge University Press, vol. 11(2), pages 195-228, February.
    3. Geert Dhaene & Christian Gourieroux & Olivier Scaillet, 1998. "Instrumental Models and Indirect Encompassing," Econometrica, Econometric Society, vol. 66(3), pages 673-688, May.
    4. 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 657-678, May.
    5. White, Halbert, 1982. "Maximum Likelihood Estimation of Misspecified Models," Econometrica, Econometric Society, vol. 50(1), pages 1-25, January.
    6. Sawa, Takamitsu, 1978. "Information Criteria for Discriminating among Alternative Regression Models," Econometrica, Econometric Society, vol. 46(6), pages 1273-1291, November.
    7. Gourieroux, C. & Monfort, A., 1986. "Testing non-nested hypotheses," Handbook of Econometrics, in: R. F. Engle & D. McFadden (ed.), Handbook of Econometrics, edition 1, volume 4, chapter 44, pages 2583-2637, Elsevier.
    8. repec:cup:etheor:v:11:y:1995:i:2:p:195-228 is not listed on IDEAS
    9. Tauchen, George, 1985. "Diagnostic testing and evaluation of maximum likelihood models," Journal of Econometrics, Elsevier, vol. 30(1-2), pages 415-443.
    10. Gourieroux, Christian & Monfort, Alain & Trognon, Alain, 1983. "Testing nested or non-nested hypotheses," Journal of Econometrics, Elsevier, vol. 21(1), pages 83-115, January.
    11. Bierens, Herman J, 1990. "A Consistent Conditional Moment Test of Functional Form," Econometrica, Econometric Society, vol. 58(6), pages 1443-1458, November.
    12. Newey, Whitney K, 1985. "Maximum Likelihood Specification Testing and Conditional Moment Tests," Econometrica, Econometric Society, vol. 53(5), pages 1047-1070, September.
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    Cited by:

    1. D. Van den Poel, 2003. "Predicting Mail-Order Repeat Buying. Which Variables Matter?," Review of Business and Economic Literature, KU Leuven, Faculty of Economics and Business (FEB), Review of Business and Economic Literature, vol. 0(3), pages 371-404.
    2. M. Neyt & J. Albrecht & B. Clarysse & V. Cocquyt, 2003. "The Cost-Effectiveness of Herceptin® in a Standard Cost Model for Breast-Cancer Treatment in a Belgian University Hospital," Working Papers of Faculty of Economics and Business Administration, Ghent University, Belgium 03/180, Ghent University, Faculty of Economics and Business Administration.

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    More about this item

    Keywords

    Score test; likelihood ratio test; encompassing; simulation-based inference;
    All these keywords.

    JEL classification:

    • C5 - Mathematical and Quantitative Methods - - Econometric Modeling
    • C3 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables

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