Uniformly More Powerful Tests in a One-Sided Multivariate Problem
单侧多变量问题中一致更有功效的检验AI 解读 ↓
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单侧多变量问题中一致更有功效的检验
- 研究问题
- 正态均值向量在零假设下为零、备择位于锥内且协方差未知时，能否改进既有似然比检验的功效和无偏性？
- 方法与思路
- 作者以包含备择锥的半空间构造相应似然比检验，通过随机序理论证明无偏性，并给出临界值及模拟比较。
- 材料陈述的贡献
- 摘要称，新检验较原锥备择似然比检验一致更有功效且更简单；相对Hotelling检验的优势仅由模拟提示。
- 阅读关注点
- 应核对一致功效改进的比较对象和参数范围、无偏性证明，以及半空间选择、协方差估计与样本量的作用。
- 阅读边界
- 仅据OpenAlex索引摘要，稿件版本未注明；不能将模拟提示升级为相对Hotelling检验的统一优势定理，具体条件未说明。
原文摘要
We consider a testing problem in which a normal mean vector is at the origin under the null hypothesis and in a cone under the alternative and the covariance matrix is unknown. Perlman studied the likelihood ratio (LR) test and found that it is biased and hence does not compare favorably with Hotelling's T2. We point out that certain tests of Perlman are uniformly more powerful as well as simpler than the LR test. These are the corresponding LR tests when the alternative is replaced with a half space that contains the cone. We prove that these tests are unbiased by developing some basic results on stochastic ordering. Critical values for these tests are given. Simulation results suggest that the new tests are also uniformly more powerful than Hotelling's T2. For the special case when the cone is the positive orthant, we discuss an issue about invariant test. Finally, we discuss the assumption of unknown covariance matrix, and conclude that the new tests are more useful for small samples than for large samples.