Abstract
Introduction:The score statisticZ(θ)and the maximin efficient robust test statisticZMERTare commonly used in genetic association study, but according to our knowledge there is no formal comparison of them.Methods:In this report, we compare the asymptotic behavior ofZ(θ)andZMERT, by computing their Asymptotic Relative Efficiencies (AREs) relative to each other. Four commonly used ARE measures, the Pitman ARE, Chernoff ARE, Hodges-Lehmann ARE and the Bahadur ARE are considered. Some modifications of these methods are made to simplify the computations. We found that the Chernoff, Hodges-Lehmann and Bahadur AREs are suitable for our setting.Results and Conclusion:Based on our study, the efficiencies of the two test statistic varies for different criterion used, and for different parameter values under the same criterion, so each test has its advantages and dis-advantages according to the criterion used and the parameters involved, which are described in the context. Numerical examples are given to illustrate the use of the two statistics in genetic association study.
Highlights
The score statistic Z(θ) and the maximin efficient robust test statistic ZMERT are commonly used in genetic association study, but according to our knowledge there is no formal comparison of them
We compare the Asymptotic Relative Efficiency (ARE) of the test statistics arose from our genetic association study. We found that he performances, or the efficiencies of the two test statistic varies for different criterion used, and for different parameter values under the same criterion, which described in the context
We focus on the statistics used in ZLY, Z(θ) and, ZMERTand refer the notations there
Summary
We compare the asymptotic behavior of Z(θ) and ZMERT, by computing their Asymptotic Relative Efficiencies (AREs) relative to each other. Four commonly used ARE measures, the Pitman ARE, Chernoff ARE, Hodges-Lehmann ARE and the Bahadur ARE are considered. Some modifications of these methods are made to simplify the computations. We found that the Chernoff, Hodges-Lehmann and Bahadur AREs are suitable for our setting
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