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

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.

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File URL: http://cowles.yale.edu/sites/default/files/files/pub/d10/d1015.pdf
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Paper provided by Cowles Foundation for Research in Economics, Yale University in its series Cowles Foundation Discussion Papers with number 1015.

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Length: 62 pages
Date of creation: Apr 1992
Publication status: Published in Econometrica (November 1994), 62(6): 1383-1414
Handle: RePEc:cwl:cwldpp:1015
Note: CFP 879.
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Web page: http://cowles.yale.edu/

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Order Information: Postal: Cowles Foundation, Yale University, Box 208281, New Haven, CT 06520-8281 USA

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  1. Saikkonen, Pentti, 1991. "Asymptotically Efficient Estimation of Cointegration Regressions," Econometric Theory, Cambridge University Press, vol. 7(01), pages 1-21, March.
  2. 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.
  3. 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.
  4. James H. Stock & Mark W. Watson, 1994. "Evidence on structural instability in macroeconomic times series relations," Working Paper Series, Macroeconomic Issues 94-13, Federal Reserve Bank of Chicago.
  5. Bruce E. Hansen, 1998. "Testing for Structural Change in Conditional Models," Boston College Working Papers in Economics 310., Boston College Department of Economics.
  6. Dufour, Jean-Marie & Kiviet, Jan F., 1996. "Exact tests for structural change in first-order dynamic models," Journal of Econometrics, Elsevier, vol. 70(1), pages 39-68, January.
  7. Simon M. Potter, 1993. "A Nonlinear Approach to U.S. GNP," UCLA Economics Working Papers 693, UCLA Department of Economics.
  8. 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.
  9. Hansen, Bruce E., 1992. "Convergence to Stochastic Integrals for Dependent Heterogeneous Processes," Econometric Theory, Cambridge University Press, vol. 8(04), pages 489-500, December.
  10. 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.
  11. Stock, James H & Watson, Mark W, 1993. "A Simple Estimator of Cointegrating Vectors in Higher Order Integrated Systems," Econometrica, Econometric Society, vol. 61(4), pages 783-820, July.
  12. 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).
  13. Engle, Robert F. & Hendry, David F., 1993. "Testing superexogeneity and invariance in regression models," Journal of Econometrics, Elsevier, vol. 56(1-2), pages 119-139, March.
  14. Peter C. B. Phillips & Mico Loretan, 1991. "Estimating Long-run Economic Equilibria," Review of Economic Studies, Oxford University Press, vol. 58(3), pages 407-436.
  15. 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.
  16. 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.
  17. Ploberger, Werner & Kramer, Walter, 1996. "A trend-resistant test for structural change based on OLS residuals," Journal of Econometrics, Elsevier, vol. 70(1), pages 175-185, January.
  18. Hendry, David F, 1988. "The Encompassing Implications of Feedback versus Feedforward Mechanisms in Econometrics," Oxford Economic Papers, Oxford University Press, vol. 40(1), pages 132-149, March.
  19. 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.
  20. Andrews, Donald W.K., 1992. "Generic Uniform Convergence," Econometric Theory, Cambridge University Press, vol. 8(02), pages 241-257, June.
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