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

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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.
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    File URL:https://cowles.yale.edu/sites/default/files/files/pub/d10/d1015.pdf
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    JEL classification:

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

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