A0558
Title: Testing stochastic block models via the maximum sampling entry-wise deviation
Authors: Wei Lan - Southwestern University of Finance and Economics (China) [presenting]
Abstract: The stochastic block model (SBM) has been widely used to analyze network data. Various goodness-of-fit tests have been proposed to assess the adequacy of model structures. To the best of our knowledge, however, none of the existing approaches is applicable for sparse networks in which the connection probability of any two communities is of order $O(n^{-1}\log n)$, and the number of communities is divergent. A novel goodness-of-fit test is proposed for the stochastic block model to fill this gap. The key idea is combining a previous test concept with a sampling process that alleviates the negative impacts of network sparsity. Theoretically, the proposed test statistic converges is demonstrated to the Type-I extreme value distribution under the null hypothesis, regardless of the network structure. Accordingly, it can be applied to both dense and sparse networks. In addition, the asymptotic power against alternatives is obtained. Moreover, a bootstrap corrected test statistic is introduced to improve the finite sample performance, recommend an augmented test statistic to increase the power and extend the proposed test to the degree-corrected SBM. Simulation studies and two empirical examples with dense and sparse networks indicate that the proposed method performs well.
