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Moreover, we develop a computational method to perform the proposed tests, which integrates an alternating direction method of multipliers and difference convex programming. Finally, the power analysis and simulations suggest that the tests achieve the desired objectives of inference. An analysis of an Alzheimer's disease gene expression dataset illustrates the utility of the proposed method to infer a directed pathway in a gene network.An amendment to this paper has been published and can be accessed via a link at the top of the paper.