HYPOTHESIS-TESTING WHEN A NUISANCE PARAMETER IS PRESENT ONLY UNDER THE ALTERNATIVE
HYPOTHESIS-TESTING WHEN A NUISANCE PARAMETER IS PRESENT ONLY UNDER THE ALTERNATIVE
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DOI：
10.1093/biomet/74.1.33
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发表时间：
1987-03-01
期刊：
影响因子：
2.7
通讯作者：
DAVIES, RB
中科院分区：
文献类型：
--
作者：
DAVIES, RB
我们希望用一个一维参数θ来检验一个简单的假设。我们使用一个检验，它来自于适用于θ给定情况的相应的检验统计量族。Davies（1977）在这些检验统计量具有正态分布时引入了这个问题。本文考虑的情况下，他们的分布是卡方。结果被应用到检测的离散频率分量的未知频率的时间序列。此外，快速的方法找到近似的显着性概率的正常和卡方的情况下，并适用于两阶段回归问题的正常情况下。
We wish to test a simple hypothesis against a family of alternatives indexed by a one-dimensional parameter, θ. We use a test derived from the corresponding family of test statistics appropriate for the case when θ is given. Davies (1977) introduced this problem when these test statistics had normal distributions. The present paper considers the case when their distribution is chi-squared. The results are applied to the detection of a discrete frequency component of unknown frequency in a time series. In addition quick methods for finding approximate significance probabilities are given for both the normal and chi-squared cases and applied to the two-phase regression problem in the normal case.