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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.

Suggested Citation

  • King, Maxwell L & Shively, Thomas S, 1993. "Locally Optimal Testing When a Nuisance Parameter Is Present Only under the Alternative," The Review of Economics and Statistics, MIT Press, vol. 75(1), pages 1-7, February.
  • Handle: RePEc:tpr:restat:v:75:y:1993:i:1:p:1-7
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    Citations

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    Cited by:

    1. 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.
    2. Sergei Koulayev & Marc Rysman & Scott Schuh & Joanna Stavins, 2016. "Explaining adoption and use of payment instruments by US consumers," RAND Journal of Economics, RAND Corporation, vol. 47(2), pages 293-325, May.
    3. Rahman, Shahidur & King, Maxwell L., 1997. "Marginal-likelihood score-based tests of regression disturbances in the presence of nuisance parameters," Journal of Econometrics, Elsevier, vol. 82(1), pages 81-106.
    4. Gao, Jiti, 2007. "Nonlinear time series: semiparametric and nonparametric methods," MPRA Paper 39563, University Library of Munich, Germany, revised 01 Sep 2007.
    5. 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.
    6. Maxwell L. King & Sivagowry Sriananthakumar, 2015. "Point Optimal Testing: A Survey of the Post 1987 Literature," Monash Econometrics and Business Statistics Working Papers 5/15, Monash University, Department of Econometrics and Business Statistics.
    7. Nektarios Aslanidis & Anastasios Xepapadeas, 2004. "Smooth ‘inverted-V-shaped’ & smooth ‘N-shaped’ pollution-income paths," Working Papers 0405, University of Crete, Department of Economics.
    8. Andrews, Donald W. K. & Lee, Inpyo & Ploberger, Werner, 1996. "Optimal changepoint tests for normal linear regression," Journal of Econometrics, Elsevier, vol. 70(1), pages 9-38, January.
    9. Hansen, Bruce E., 2000. "Testing for structural change in conditional models," Journal of Econometrics, Elsevier, vol. 97(1), pages 93-115, July.
    10. Harvey, Andrew & Streibel, Mariane, 1998. "Testing for a slowly changing level with special reference to stochastic volatility," Journal of Econometrics, Elsevier, vol. 87(1), pages 167-189, August.
    11. Maciejowska, Katarzyna, 2013. "Assessing the number of components in a normal mixture: an alternative approach," MPRA Paper 50303, University Library of Munich, Germany.

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