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. 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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Volume (Year): 62 (1994)
Issue (Month): 6 (November)
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Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- 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.
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Cowles Foundation Discussion Papers
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"Tests for Parameter Instability in Regressions with I(1) Processes,"
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American Statistical Association, vol. 10(3), pages 321-35, July.
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- 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.
- 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.
- 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.
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