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

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Author Info
Donald W.K. Andrews () (Cowles Foundation, Yale University)

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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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Publisher Info
Paper provided by Cowles Foundation, 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
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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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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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References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Andrews, Donald W. K., 1998. "Hypothesis testing with a restricted parameter space," Journal of Econometrics, Elsevier, vol. 84(1), pages 155-199, May. [Downloadable!] (restricted)
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  2. Andrews, Donald W K, 1994. "Asymptotics for Semiparametric Econometric Models via Stochastic Equicontinuity," Econometrica, Econometric Society, vol. 62(1), pages 43-72, January. [Downloadable!] (restricted)
  3. 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. [Downloadable!] (restricted)
  4. 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. [Downloadable!] (restricted)
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