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Abstract:
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In this talk, we present some limiting theory and numerical results for approximating the distribution of network U-statistics in presence of edge-wise random noise. We compare the results with the classical noiseless setting and discuss their connections and differences. We derive the first higher order accuracy term in the Edgeworth approximation and show an explicit uniform error bound for the remainder under mild sparsity and other conditions. Specifically, we discovered that the roles of sparsity and random edge noise to be blessing in smoothing out periodicity in the case that Cramer's condition, which has always been assumed in the noiseless case but is violated by some most frequently studied network models such as stochastic block model, fails. We also discuss the nonparametric bootstrap's performance and compared our method's accuracy with it.
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