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Optimal Tests When A Nuisance Parameter Is Present Only Under The Alternative, Donald W.K. Andrews, Werner Ploberger
Optimal Tests When A Nuisance Parameter Is Present Only Under The Alternative, Donald W.K. Andrews, Werner Ploberger
Cowles Foundation Discussion Papers
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.