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Abstract:
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Two nonparametric methods for high-dimensional inference are proposed. By high-dimensional is meant both the sample size and dimension tend to infinity, possibly at different rate. When it is reasonable to formulate treatment effects in terms of cell means, asymptotic expansion of moments of a composite t^2-based statistic are used to get accurate tests. Otherwise, it is nonparametric in the sense that no distributional assumption is made for the development of the test. On the contrary, there are situations where cell-mean based inference is not appropriate. For example, when data is observed in ordinal scale or when the underlying distribution is heavy tailed. For these situations, we developed a fully-nonparametric high-dimensional test for the multivariate version of Wilcoxon-Mann-Whitney effects. The theory in this case only requires mild mixing-type assumptions to regulate the dependence. Numerical results show that both tests control the sizes reasonably well and have favorable power performance compared to other methods, in particular, for diffuse-type alternatives. Data from Electroencephalograph (EEG) experiment is analyzed as an illustrative example.
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