OPTIMAL TESTS WHEN A NUISANCE PARAMETER IS PRESENT ONLY UNDER THE ALTERNATIVE
OPTIMAL TESTS WHEN A NUISANCE PARAMETER IS PRESENT ONLY UNDER THE ALTERNATIVE
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DOI：
10.2307/2951753
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发表时间：
1994-11-01
期刊：
影响因子：
6.1
通讯作者：
PLOBERGER, W
中科院分区：
文献类型：
--
作者：
ANDREWS, DWK;PLOBERGER, W
本文导出了在备择假设下存在讨厌参数但在零值假设下不存在讨厌参数的检验问题的渐近最优检验。 例如，该结果适用于未知变点的一次性结构变化的检验。 文中还讨论了其他几个例子。 本文的结果是有趣的，因为考虑的测试问题是非标准的和经典的渐近最优性结果的拉格朗日（LM），Wald和似然比（LR）测试不适用. 这个准则类似于Wald（1943）在“正则”检验问题中获得Wald检验的经典渐近最优性的准则。 事实上，当标准正则性条件成立时，这里介绍的最优检验简化为标准LM、Wald和LR检验。 然而，在非标准的情况下，主要的利益，新的最佳测试，LR测试是不是一个最佳的测试。
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 one-time structural change with unknown change-point. Several other examples are discussed in the paper. The results of the paper are of interest, because the testing problem considered is nonstandard and the classical asymptotic optimality results for the Lagrange multiplier (LM), Wald, and likelihood ratio (LR) tests do not apply.A weighted average power criterion is used here to generate optimal tests. This criterion is similar to that used by Wald (1943) to obtain the classical asymptotic optimality properties of Wald tests in ''regular'' testing problems. In fact, the optimal tests introduced here reduce to the standard LM, Wald, and LR tests when standard regularity conditions hold. Nevertheless, in the nonstandard cases of main interest, new optimal tests are obtained and the LR test is not found to be an optimal test.