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Hypothesis Testing with a Restricted Parameter Space

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This paper considers hypothesis tests for nonlinear econometric models when the parameter space is restricted under the alternative hypothesis. Multivariate one-sided tests are a leading example. Asymptotically optimal tests are derived using a weighted average power criterion. In addition, the likelihood ratio test is shown to be asymptotically admissible and to maximize asymptotic power against alternatives that are arbitrarily distant from the null hypothesis. For Gaussian linear regression models with known variance, analogous exact finite sample results are established.

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File URL: http://cowles.econ.yale.edu/P/cd/d10b/d1060-r.pdf
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Paper provided by Cowles Foundation for Research in Economics, Yale University in its series Cowles Foundation Discussion Papers with number 1060R.

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Length: 63 pages
Date of creation: Jun 1994
Date of revision:
Publication status: Published in Journal of Econometrics (1998), 84: 155-199
Handle: RePEc:cwl:cwldpp:1060r

Note: CFP 960.
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Postal: Yale University, Box 208281, New Haven, CT 06520-8281 USA
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Web page: http://cowles.econ.yale.edu/
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  1. 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.
  2. Dufour, Jean-Marie, 1989. "Nonlinear Hypotheses, Inequality Restrictions, and Non-nested Hypotheses: Exact Simultaneous Tests in Linear Regressions," Econometrica, Econometric Society, vol. 57(2), pages 335-55, March.
  3. Hillier, Grant, 1986. "Joint Tests for Zero Restrictions on Non-negative Regression Coefficients," MPRA Paper 15804, University Library of Munich, Germany.
  4. Gourieroux, Christian & Holly, Alberto & Monfort, Alain, 1982. "Likelihood Ratio Test, Wald Test, and Kuhn-Tucker Test in Linear Models with Inequality Constraints on the Regression Parameters," Econometrica, Econometric Society, vol. 50(1), pages 63-80, January.
  5. Rogers, Alan J., 1986. "Modified lagrange multiplier tests for problems with one-sided alternatives," Journal of Econometrics, Elsevier, vol. 31(3), pages 341-361, April.
  6. Wolak, Frank A., 1989. "Local and Global Testing of Linear and Nonlinear Inequality Constraints in Nonlinear Econometric Models," Econometric Theory, Cambridge University Press, vol. 5(01), pages 1-35, April.
  7. Wolak, Frank A., 1989. "Testing inequality constraints in linear econometric models," Journal of Econometrics, Elsevier, vol. 41(2), pages 205-235, June.
  8. Andrews, Donald W K, 1996. "Admissibility of the Likelihood Ratio Test When the Parameter Space Is Restricted under the Alternative," Econometrica, Econometric Society, vol. 64(3), pages 705-18, May.
  9. Kodde, David A & Palm, Franz C, 1986. "Wald Criteria for Jointly Testing Equality and Inequality Restriction s," Econometrica, Econometric Society, vol. 54(5), pages 1243-48, September.
  10. Maxwell King & Ping Wu, 1997. "Locally optimal one-sided tests for multiparameter hypotheses," Econometric Reviews, Taylor & Francis Journals, vol. 16(2), pages 131-156.
  11. King, Maxwell L. & Smith, Murray D., 1986. "Joint one-sided tests of linear regression coefficients," Journal of Econometrics, Elsevier, vol. 32(3), pages 367-383, August.
  12. Hajivassiliou, Vassilis & McFadden, Daniel & Ruud, Paul, 1996. "Simulation of multivariate normal rectangle probabilities and their derivatives theoretical and computational results," Journal of Econometrics, Elsevier, vol. 72(1-2), pages 85-134.
  13. Donald W.K. Andrews, 1990. "Generic Uniform Convergence," Cowles Foundation Discussion Papers 940, Cowles Foundation for Research in Economics, Yale University.
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