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

  • Andrews, Donald W K
  • Ploberger, Werner

This paper derives asymptotically optimal tests for testing problems in which a nuisance parameter exists under the alternative hypothesis but not under the null. For example, the results apply to tests of structural change with unknown changepoint. The testing problem considered is nonstandard and the classical asymptotic optimality results for the Lagrange multiplier, Wald, and likelihood ratio do not apply. A weighted average power criterion is used here to generate optimal tests. This criterion is similar to that used by A. Wald (1943) to obtain the classical asymptotic optimality properties of Wald tests in 'regular' testing problems. Copyright 1994 by The Econometric Society.

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Article provided by Econometric Society in its journal Econometrica.

Volume (Year): 62 (1994)
Issue (Month): 6 (November)
Pages: 1383-1414

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Handle: RePEc:ecm:emetrp:v:62:y:1994:i:6:p:1383-1414
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  1. 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.
  2. Hansen, B.E., 1991. "Inference when a Nuisance Parameter is Not Identified Under the Null Hypothesis," RCER Working Papers 296, University of Rochester - Center for Economic Research (RCER).
  3. Andrews, Donald W.K., 1992. "Generic Uniform Convergence," Econometric Theory, Cambridge University Press, vol. 8(02), pages 241-257, June.
  4. 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.
  5. 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.
  6. Simon M. Potter, 1993. "A Nonlinear Approach to U.S. GNP," UCLA Economics Working Papers 693, UCLA Department of Economics.
  7. 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.
  8. 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.
  9. 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 1465-71, November.
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