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Testing When a Parameter Is on the Boundary of the Maintained Hypothesis

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Abstract

This paper considers testing problems where several of the standard regularity conditions fail to hold. We consider the case where (i) parameter vectors in the null hypothesis may lie on the boundary of the maintained hypothesis and (ii) there may be a nuisance parameter that appears under the alternative hypothesis, but not under the null. The paper establishes the asymptotic null and local alternative distributions of quasi-likelihood ratio, rescaled quasi-likelihood ratio, Wald, and score tests in this case. The results apply to tests based on a wide variety of extremum estimators and apply to a wide variety of models. Examples treated in the paper are: (1) tests of the null hypothesis of no conditional heteroskedasticity in a GARCH(1, 1) regression model and (2) tests of the null hypothesis that some random coefficients have variances equal to zero in a random coefficients regression model with (possibly) correlated random coefficients.

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File URL: http://cowles.econ.yale.edu/P/cd/d12a/d1229.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 1229.

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Length: 50 pages
Date of creation: Jul 1999
Date of revision:
Publication status: Published in Econometrics (2001), 69(3): 683-734
Handle: RePEc:cwl:cwldpp:1229

Note: CFP 1021.
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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

Related research

Keywords: Asymptotic distribution; boundary; conditional heteroskedasticity; extremum estimator; GARCH model; inequality restrictions; likelihood ratio test; local power; maximum likelihood estimator; parameter restrictions; random coefficients regression; quasi-maximum likelihood estimator; quasi-likelihood ratio test; restricted estimator; score test; Wald test;

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  1. 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.
  2. Pollard, David, 1985. "New Ways to Prove Central Limit Theorems," Econometric Theory, Cambridge University Press, vol. 1(03), pages 295-313, December.
  3. Andrews, Donald W K, 1994. "Asymptotics for Semiparametric Econometric Models via Stochastic Equicontinuity," Econometrica, Econometric Society, vol. 62(1), pages 43-72, January.
  4. Donald W.K. Andrews, 1994. "Hypothesis Testing with a Restricted Parameter Space," Cowles Foundation Discussion Papers 1060R, Cowles Foundation for Research in Economics, Yale University.
  5. 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.
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