Before revision:  In sharp contrast to classical literature on noiseless U-statistics, we showed that the Edgeworth expansion of a network moment statistic as a noisy U-statistic can achieve higher-order accuracy without non-lattice or smoothness assumptions but just requiring weak regularity conditions.
After revision:  In sharp contrast to classical literature on noiseless U-statistics, we show that the Edgeworth expansion of a network moment statistic as a noisy U-statistic can achieve higher-order accuracy without non-lattice or smoothness assumptions but just requiring weak regularity conditions.