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Abstract:
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Numerous statistical methods have been developed for analyzing high-dimensional data. These methods often focus on variable selection approaches but are limited for the purpose of testing with high-dimensional data. They are often required to have explicit likelihood functions. In this paper, we propose a kernel based-hybrid omnibus test for high-dimensional data testing purpose with much weaker requirements. Our hybrid omnibus test is developed under a semiparametric framework where a likelihood function is no longer necessary. Our test is a version of a frequentist-Bayesian hybrid score-type test for a nonparametric model, which has a link function being a functional of a set of variables through Gaussian processes with high correlated variables. We propose an efficient score based on estimating equations and then construct our hybrid omnibus test using local tests. We compare our approach with an empirical likelihood ratio test and Bayesian inference based on Bayes factors, using simulation studies. The advantage of our approach is demonstrated by applying it to genetic pathway data for type II diabetes mellitus.
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