Asymptotic power comparison of T2-type test and likelihood ratio test for a mean vector based on two-step monotone missing data

Masashi Hyodo and Nobumichi Shutoh

Communications in Statistics - Theory and Methods, 2020, vol. 49, issue 17, 4270-4287

Abstract: In a 2-step monotone missing dataset drawn from a multivariate normal population, T2-type test statistic (similar to Hotelling’s T2 test statistic) and likelihood ratio (LR) are often used for the test for a mean vector. In complete data, Hotelling’s T2 test and LR test are equivalent, however T2-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 and T2-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.

Date: 2020
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DOI: 10.1080/03610926.2019.1597122

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