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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.

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File URL: http://cowles.econ.yale.edu/P/cd/d10b/d1058.pdf
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Bibliographic Info

Paper provided by Cowles Foundation for Research in Economics, Yale University in its series Cowles Foundation Discussion Papers with number 1058.

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Length: 32 pages
Date of creation: Jul 1993
Date of revision:
Publication status: Published in Annals of Statistics (1995), 23(5): 1609-1629
Handle: RePEc:cwl:cwldpp:1058

Note: CFP 916.
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Postal: Yale University, Box 208281, New Haven, CT 06520-8281 USA
Phone: (203) 432-3702
Fax: (203) 432-6167
Web page: http://cowles.econ.yale.edu/
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Postal: Cowles Foundation, Yale University, Box 208281, New Haven, CT 06520-8281 USA

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References

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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., 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.
  3. 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.
  4. Donald W.K. Andrews & Inpyo Lee & Werner Ploberger, 1992. "Optimal Changepoint Tests for Normal Linear Regression," Cowles Foundation Discussion Papers 1016, Cowles Foundation for Research in Economics, Yale University.
  5. Andrews, Donald W K, 1993. "Tests for Parameter Instability and Structural Change with Unknown Change Point," Econometrica, Econometric Society, vol. 61(4), pages 821-56, July.
  6. 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.
  7. 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.
  8. 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.
  9. 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.
  10. repec:cup:etheor:v:8:y:1992:i:2:p:241-57 is not listed on IDEAS
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Citations

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Cited by:
  1. 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 763-88, August.
  2. 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.
  3. 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.
  4. 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, School of Economics and Management, University of Aarhus.
  5. Jonathan Hill, 2006. "Asymptotically Nuisance-Parameter-Free Consistent Tests of Lp-Functional Form," Working Papers 0608, Florida International University, Department of Economics.
  6. Jonathan B. Hill, 2004. "Consistent and Non-Degenerate Model Specification Tests Against Smooth Transition Alternatives," Working Papers 0406, Florida International University, Department of Economics.
  7. 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.
  8. 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.
  9. 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.

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