Hypothesis Testing for Network Data with Power Enhancement
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Comparing two population means of network data is of paramount importance in a wide range of scientific applications. Most existing network inference solutions focus on the scenario when the observed data are vectors or matrices, and formulate the network comparison problem as comparing two covariance or precision matrices under a normal or matrix normal distribution. Moreover, many suffer from a limited power under a small sample size. In this article, we tackle the problem of network comparison when the data come in a different format, i.e., in the form of a collection of symmetric matrices, each of which encodes the network structure of an individual subject. Such data format commonly arises in applications such as brain connectivity analysis and clinical genomics. We no longer require the underlying data to follow a normal distribution, but instead impose some moment conditions that are easily satisfied for numerous types of network data. Furthermore, we propose a power enhancement procedure, and show that it can control the false discovery, while it has the potential to substantially enhance the power of the test. We investigate the efficacy of our testing procedure through both an asymptotic analysis, and a simulation study under a finite sample size. We further illustrate our method with an example of brain structural connectivity analysis.
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