Asymptotic power comparison of T2-type test and likelihood ratio test for a mean vector based on two-step monotone missing data
Asymptotic power comparison of T2-type test and likelihood ratio test for a mean vector based on two-step monotone missing data
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基于两步单调缺失数据的均值向量T2型检验与似然比检验的渐近功效比较
DOI：
10.1080/03610926.2019.1597122
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发表时间：
2019
期刊：
影响因子：
--
通讯作者：
Shutoh Nobumichi
中科院分区：
文献类型：
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作者：
Hyodo Masashi;Shutoh Nobumichi
在多变量正态总体的两步单调缺失数据集中，T2检验统计量（类似于Hotelling的T2检验统计量）和似然比（LR）常用于均值向量的检验。在完全数据下，Hotelling的T2检验与LR检验是等价的，而在两步单调缺失数据下，T2检验与LR检验是不等价的。然后，我们感兴趣的统计是合理的权力。本文导出了这两种统计量在局部选择下的渐近幂函数，并得到了渐近幂函数差的显式表达式。此外，在多种参数设置下，利用经验幂函数和渐进幂函数的差异，对LR和T2型检验进行了数值比较。总结所获得的结果，我们建议应用LR测试的平均向量。
In a 2-step monotone missing dataset drawn from a multivariate normal population,T2-type test statistic (similar to Hotelling’sT2test statistic) and likelihood ratio (LR) are often used for the test for a mean vector. In complete data, Hotelling’sT2test and LR test are equivalent, howeverT2-type test and LR test are not equivalent in the 2-step monotone missing dataset. Then we interest which statistic is reasonable with relation to power. In this paper, we derive asymptotic power function of both statistics under a local alternative and obtain an explicit form for difference in asymptotic power function. Furthermore, under several parameter settings, we compare LR andT2-type test numerically by using difference in empirical power and in asymptotic power function. Summarizing obtained results, we recommend applying LR test for testing a mean vector.