Testing for positive expectation dependence

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Annals of the Institute of Statistical Mathematics, ISSN: 1572-9052, Vol: 68, Issue: 1, Page: 135-153

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Zhu, Xuehu; Guo, Xu; Lin, Lu; Zhu, Lixing
Springer Nature; Springer Verlag
Mathematics; Expectation dependence; Nonparametric Monte Carlo; Test of Kolmogorov–Smirnov type
article description
In this paper, hypothesis testing for positive first-degree and higher-degree expectation dependence is investigated. Some tests of Kolmogorov–Smirnov type are constructed, which are shown to control type I error well and to be consistent against global alternative hypothesis. Further, the tests can also detect local alternative hypotheses distinct from the null hypothesis at a rate as close to the square root of the sample size as possible, which is the fastest possible rate in hypothesis testing. A nonparametric Monte Carlo test procedure is applied to implement the new tests because both sampling and limiting null distributions are not tractable. Simulation studies and a real data analysis are carried out to illustrate the performances of the new tests.