Testing When a Parameter Is on the Boundary of the Maintained Hypothesis
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.
|Date of creation:||Jul 1999|
|Date of revision:|
|Publication status:||Published in Econometrics (2001), 69(3): 683-734|
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- 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.
- Andrews, Donald W. K., 1998. "Hypothesis testing with a restricted parameter space," Journal of Econometrics, Elsevier, vol. 84(1), pages 155-199, May.
- Pollard, David, 1985. "New Ways to Prove Central Limit Theorems," Econometric Theory, Cambridge University Press, vol. 1(03), pages 295-313, December.
- Andrews, Donald W K, 1993.
"Tests for Parameter Instability and Structural Change with Unknown Change Point,"
Econometric Society, vol. 61(4), pages 821-56, July.
- Donald W.K. Andrews, 1990. "Tests for Parameter Instability and Structural Change with Unknown Change Point," Cowles Foundation Discussion Papers 943, Cowles Foundation for Research in Economics, Yale University.
- Andrews, Donald W K, 1994. "Asymptotics for Semiparametric Econometric Models via Stochastic Equicontinuity," Econometrica, Econometric Society, vol. 62(1), pages 43-72, January.
- 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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