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Admissibility of the Likelihood Ratio Test When a Nuisance Parameter Is Present OnlyUnder the Alternative

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Abstract

This paper establishes the asymptotic admissibility of the likelihood ratio (LR) test for a general class of testing problems in which a nuisance parameter is present only under the alternative hypothesis. The paper also establishes the finite sample admissibility of the LR test for testing problems of this sort that arise in Gaussian linear regression models with known variance.

Suggested Citation

  • Donald W.K. Andrews & Werner Ploberger, 1993. "Admissibility of the Likelihood Ratio Test When a Nuisance Parameter Is Present OnlyUnder the Alternative," Cowles Foundation Discussion Papers 1058, Cowles Foundation for Research in Economics, Yale University.
  • Handle: RePEc:cwl:cwldpp:1058
    Note: CFP 916.
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    File URL: http://cowles.yale.edu/sites/default/files/files/pub/d10/d1058.pdf
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    References listed on IDEAS

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    1. Andrews, Donald W.K., 1992. "Generic Uniform Convergence," Econometric Theory, Cambridge University Press, vol. 8(02), pages 241-257, June.
    2. Andrews, Donald W. K. & Lee, Inpyo & Ploberger, Werner, 1996. "Optimal changepoint tests for normal linear regression," Journal of Econometrics, Elsevier, vol. 70(1), pages 9-38, January.
    3. Perron, P., 1991. "A Test for Changes in a Polynomial Trend Functions for a Dynamioc Time Series," Papers 363, Princeton, Department of Economics - Econometric Research Program.
    4. Andrews, Donald W.K., 1986. "Empirical process methods in econometrics," Handbook of Econometrics,in: R. F. Engle & D. McFadden (ed.), Handbook of Econometrics, edition 1, volume 4, chapter 37, pages 2247-2294 Elsevier.
    5. repec:cup:etheor:v:8:y:1992:i:2:p:241-57 is not listed on IDEAS
    6. Andrews, Donald W K, 1993. "Tests for Parameter Instability and Structural Change with Unknown Change Point," Econometrica, Econometric Society, vol. 61(4), pages 821-856, July.
    7. Hansen, Bruce E., 2000. "Testing for structural change in conditional models," Journal of Econometrics, Elsevier, vol. 97(1), pages 93-115, July.
    8. Andrews, Donald W K & Ploberger, Werner, 1994. "Optimal Tests When a Nuisance Parameter Is Present Only under the Alternative," Econometrica, Econometric Society, vol. 62(6), pages 1383-1414, November.
    9. Robert B. Davies, 2002. "Hypothesis testing when a nuisance parameter is present only under the alternative: Linear model case," Biometrika, Biometrika Trust, vol. 89(2), pages 484-489, June.
    10. Donald W.K. Andrews, 1986. "Consistency in Nonlinear Econometric Models: A Generic Uniform Law of Large Numbers," Cowles Foundation Discussion Papers 790, Cowles Foundation for Research in Economics, Yale University.
    11. Ploberger, Werner & Kramer, Walter & Kontrus, Karl, 1989. "A new test for structural stability in the linear regression model," Journal of Econometrics, Elsevier, vol. 40(2), pages 307-318, February.
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    Cited by:

    1. Donald W.K. Andrews & Liu, Xuemei Liu & Werner Ploberger, 1996. "Tests of Seasonal and Non-Seasonal Serial Correlation," Cowles Foundation Discussion Papers 1124, Cowles Foundation for Research in Economics, Yale University.
    2. Garcia, Rene, 1998. "Asymptotic Null Distribution of the Likelihood Ratio Test in Markov Switching Models," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(3), pages 763-788, August.
    3. Francq, Christian & Horvath, Lajos & Zakoian, Jean-Michel, 2008. "Sup-tests for linearity in a general nonlinear AR(1) model when the supremum is taken over the full parameter space," MPRA Paper 16669, University Library of Munich, Germany.
    4. Kim, Dukpa & Perron, Pierre, 2009. "Assessing the relative power of structural break tests using a framework based on the approximate Bahadur slope," Journal of Econometrics, Elsevier, vol. 149(1), pages 26-51, April.
    5. Beard, T. Randolph & Caudill, Steven B. & Gropper, Daniel M., 1997. "The diffusion of production processes in the U.S. banking industry: A finite mixture approach," Journal of Banking & Finance, Elsevier, vol. 21(5), pages 721-740, May.
    6. Tue Gørgens & Christopher L. Skeels & Allan H. Würtz, 2009. "Efficient Estimation of Non-Linear Dynamic Panel Data Models with Application to Smooth Transition Models," CREATES Research Papers 2009-51, Department of Economics and Business Economics, Aarhus University.
    7. Donald W.K. Andrews & Werner Ploberger, 1994. "Testing for Serial Correlation Against an ARMA(1,1) Process," Cowles Foundation Discussion Papers 1077, Cowles Foundation for Research in Economics, Yale University.

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