IDEAS home Printed from https://ideas.repec.org/p/cwl/cwldpp/1015.html
   My bibliography  Save this paper

Optimal Tests When a Nuisance Parameter Is Present Only Under the Alternative

Author

Abstract

This paper derives asymptotically optimal tests for testing problems in which a nuisance parameter exists under the alternative hypothesis but not under the null. The results of the paper are of interest, because the testing problem considered in non-standard and the classical asymptotic optimality results for the Wald, Lagrange multiplier (LM), and likelihood ratio (LR) tests do not apply. In the non-standard cases of main interest, new optimal tests are obtained and the LR test is not found to be an optimal test.

Suggested Citation

  • Donald W.K. Andrews & Werner Ploberger, 1992. "Optimal Tests When a Nuisance Parameter Is Present Only Under the Alternative," Cowles Foundation Discussion Papers 1015, Cowles Foundation for Research in Economics, Yale University.
  • Handle: RePEc:cwl:cwldpp:1015
    Note: CFP 879.
    as

    Download full text from publisher

    File URL: https://cowles.yale.edu/sites/default/files/files/pub/d10/d1015.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. James M. Nason, 1991. "The permanent income hypothesis when the bliss point is stochastic," Discussion Paper / Institute for Empirical Macroeconomics 46, Federal Reserve Bank of Minneapolis.
    2. Andrews, Donald W K, 1987. "Consistency in Nonlinear Econometric Models: A Generic Uniform Law of Large Numbers [On Unification of the Asymptotic Theory of Nonlinear Econometric Models]," Econometrica, Econometric Society, vol. 55(6), pages 1465-1471, November.
    3. 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.
    4. Hansen, Bruce E, 1996. "Inference When a Nuisance Parameter Is Not Identified under the Null Hypothesis," Econometrica, Econometric Society, vol. 64(2), pages 413-430, March.
    5. Potter, Simon M, 1995. "A Nonlinear Approach to US GNP," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 10(2), pages 109-125, April-Jun.
    6. 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.
    7. Andrews, Donald W.K., 1992. "Generic Uniform Convergence," Econometric Theory, Cambridge University Press, vol. 8(2), pages 241-257, June.
    8. Donald W.K. Andrews & Werner Ploberger, 1994. "Testing for Serial Correlation Against an ARMA(1,1) Process," Cowles Foundation Discussion Papers 1077, Cowles Foundation for Research in Economics, Yale University.
    9. Hansen, Bruce E, 2002. "Tests for Parameter Instability in Regressions with I(1) Processes," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 45-59, January.
    10. Andrews, Donald W K, 1993. "Tests for Parameter Instability and Structural Change with Unknown Change Point," Econometrica, Econometric Society, vol. 61(4), pages 821-856, July.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Donald W.K. Andrews, 1992. "An Introduction to Econometric Applications of Functional Limit Theory for Dependent Random Variables," Cowles Foundation Discussion Papers 1020, Cowles Foundation for Research in Economics, Yale University.
    2. Hansen,B.E., 1999. "Testing for linearity," Working papers 7, Wisconsin Madison - Social Systems.
    3. Donald W.K. Andrews & Werner Ploberger, 1994. "Testing for Serial Correlation Against an ARMA(1,1) Process," Cowles Foundation Discussion Papers 1077, Cowles Foundation for Research in Economics, Yale University.
    4. Yu, Ping & Phillips, Peter C.B., 2018. "Threshold regression with endogeneity," Journal of Econometrics, Elsevier, vol. 203(1), pages 50-68.
    5. Mehmet Caner & Bruce E. Hansen, 1998. "Threshold Autoregressions with a Near Unit Root," Working Papers 9821, Department of Economics, Bilkent University.
    6. Sandberg, Rickard, 2016. "Trends, unit roots, structural changes, and time-varying asymmetries in U.S. macroeconomic data: the Stock and Watson data re-examined," Economic Modelling, Elsevier, vol. 52(PB), pages 699-713.
    7. 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.
    8. Carrasco, Marine, 2002. "Misspecified Structural Change, Threshold, and Markov-switching models," Journal of Econometrics, Elsevier, vol. 109(2), pages 239-273, August.
    9. Jesús Gonzalo & Jean‐Yves Pitarakis, 2006. "Threshold Effects in Cointegrating Relationships," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 68(s1), pages 813-833, December.
    10. Meitz, Mika & Saikkonen, Pentti, 2021. "Testing for observation-dependent regime switching in mixture autoregressive models," Journal of Econometrics, Elsevier, vol. 222(1), pages 601-624.
    11. Hinich, Melvin J. & Foster, John & Wild, Phillip, 2006. "Structural change in macroeconomic time series: A complex systems perspective," Journal of Macroeconomics, Elsevier, vol. 28(1), pages 136-150, March.
    12. Lanouar Charfeddine & Dominique Guegan, 2008. "Is it possible to discriminate between different switching regressions models? An empirical investigation," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00368358, HAL.
    13. Ghysels, Eric & Guay, Alain, 2003. "Structural change tests for simulated method of moments," Journal of Econometrics, Elsevier, vol. 115(1), pages 91-123, July.
    14. Lanouar Charfeddine & Dominique Guegan, 2008. "Is it possible to discriminate between different switching regressions models? An empirical investigation," Post-Print halshs-00368358, HAL.
    15. 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.
    16. Francq, Christian & Horvath, Lajos & Zakoïan, Jean-Michel, 2010. "Sup-Tests For Linearity In A General Nonlinear Ar(1) Model," Econometric Theory, Cambridge University Press, vol. 26(4), pages 965-993, August.
    17. Koop, Gary & Potter, Simon M., 1998. "Bayes factors and nonlinearity: Evidence from economic time series1," Journal of Econometrics, Elsevier, vol. 88(2), pages 251-281, November.
    18. Donald W.K. Andrews & Werner Ploberger, 1993. "Admissibility of the Likelihood Ratio Test When a Nuisance Parameter Is Present OnlyUnder the Alternative," Cowles Foundation Discussion Papers 1058, Cowles Foundation for Research in Economics, Yale University.
    19. Anne Morrison Piehl & Suzanne J. Cooper & Anthony A. Braga & David M. Kennedy, 2003. "Testing for Structural Breaks in the Evaluation of Programs," The Review of Economics and Statistics, MIT Press, vol. 85(3), pages 550-558, August.
    20. Sun, Yanpeng & Song, Yuru & Long, Chi & Qin, Meng & Lobonţ, Oana-Ramona, 2023. "How to improve global environmental governance? Lessons learned from climate risk and climate policy uncertainty," Economic Analysis and Policy, Elsevier, vol. 80(C), pages 1666-1676.

    More about this item

    Keywords

    Asymptotics; changepoint; nonstandard testing problem;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:cwl:cwldpp:1015. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Brittany Ladd (email available below). General contact details of provider: https://edirc.repec.org/data/cowleus.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.