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Hypothesis testing with a restricted parameter space

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  • Andrews, Donald W. K.

Abstract

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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  • Andrews, Donald W. K., 1998. "Hypothesis testing with a restricted parameter space," Journal of Econometrics, Elsevier, vol. 84(1), pages 155-199, May.
  • Handle: RePEc:eee:econom:v:84:y:1998:i:1:p:155-199
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    1. 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.
    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 335-355, March.
    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. Kodde, David A & Palm, Franz C, 1986. "Wald Criteria for Jointly Testing Equality and Inequality Restriction s," Econometrica, Econometric Society, vol. 54(5), pages 1243-1248, September.
    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. Maxwell King & Ping Wu, 1997. "Locally optimal one-sided tests for multiparameter hypotheses," Econometric Reviews, Taylor & Francis Journals, vol. 16(2), pages 131-156.
    7. Andrews, Donald W.K., 1992. "Generic Uniform Convergence," Econometric Theory, Cambridge University Press, vol. 8(02), pages 241-257, June.
    8. Hillier, Grant, 1986. "Joint Tests for Zero Restrictions on Non-negative Regression Coefficients," MPRA Paper 15804, University Library of Munich, Germany.
    9. 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.
    10. Wolak, Frank A., 1989. "Testing inequality constraints in linear econometric models," Journal of Econometrics, Elsevier, vol. 41(2), pages 205-235, June.
    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. 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.
    13. Hansen, Bruce E., 2000. "Testing for structural change in conditional models," Journal of Econometrics, Elsevier, vol. 97(1), pages 93-115, July.
    14. 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 705-718, May.
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