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Locally Optimal Testing When a Nuisance Parameter Is Present Only under the Alternative

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  • King, Maxwell L
  • Shively, Thomas S

Abstract

The authors consider hypothesis testing problems in which a nuisance parameter is present only under the alternative hypothesis. Standard asymptotic tests, such as likelihood ratio, Lagrange multiplier and Wald tests, are difficult to apply because o f problems incurred in obtaining their asymptotic distributions. To overcome this difficulty, the authors reparameterize the testing problem to one for which an exact small sample test can be construct ed using existing hypothesis testing procedures. The reparameterization technique is applied to two examples from the econometrics literatur e, and an empirical power comparison shows that their test has better power properties than tests previously proposed in the literature. Further, p-values for their test can be computed. in O(n) operations so the test can be implemented efficiently. Copyright 1993 by MIT Press.

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Bibliographic Info

Article provided by MIT Press in its journal Review of Economics & Statistics.

Volume (Year): 75 (1993)
Issue (Month): 1 (February)
Pages: 1-7

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Handle: RePEc:tpr:restat:v:75:y:1993:i:1:p:1-7

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Web page: http://mitpress.mit.edu/journals/

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Cited by:
  1. Donald W.K. Andrews & Inpyo Lee & Werner Ploberger, 1992. "Optimal Changepoint Tests for Normal Linear Regression," Cowles Foundation Discussion Papers, Cowles Foundation for Research in Economics, Yale University 1016, Cowles Foundation for Research in Economics, Yale University.
  2. Harvey, Andrew & Streibel, Mariane, 1998. "Testing for a slowly changing level with special reference to stochastic volatility," Journal of Econometrics, Elsevier, Elsevier, vol. 87(1), pages 167-189, August.
  3. Gao, Jiti, 2007. "Nonlinear time series: semiparametric and nonparametric methods," MPRA Paper 39563, University Library of Munich, Germany, revised 01 Sep 2007.
  4. Nektarios Aslanidis & Anastasios Xepapadeas, 2004. "Smooth ‘inverted-V-shaped’ & smooth ‘N-shaped’ pollution-income paths," Working Papers, University of Crete, Department of Economics 0405, University of Crete, Department of Economics.
  5. Francq, Christian & Horvath, Lajos & Zakoian, Jean-Michel, 2008. "Sup-tests for linearity in a general nonlinear AR(1) model when the supremum is taken over the full parameter space," MPRA Paper 16669, University Library of Munich, Germany.
  6. Andrews, Donald W K & Ploberger, Werner, 1994. "Optimal Tests When a Nuisance Parameter Is Present Only under the Alternative," Econometrica, Econometric Society, Econometric Society, vol. 62(6), pages 1383-1414, November.
  7. Jonathan Hill, 2006. "Super-Consistent Tests of Lp-Functional Form," Working Papers, Florida International University, Department of Economics 0610, Florida International University, Department of Economics.
  8. Rahman, Shahidur & King, Maxwell L., 1997. "Marginal-likelihood score-based tests of regression disturbances in the presence of nuisance parameters," Journal of Econometrics, Elsevier, Elsevier, vol. 82(1), pages 81-106.
  9. Maciejowska, Katarzyna, 2013. "Assessing the number of components in a normal mixture: an alternative approach," MPRA Paper 50303, University Library of Munich, Germany.
  10. Jonathan B. Hill, 2004. "Consistent and Non-Degenerate Model Specification Tests Against Smooth Transition Alternatives," Working Papers, Florida International University, Department of Economics 0406, Florida International University, Department of Economics.

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