Adjusted chi-square test for degree-corrected block models. (arXiv:2012.15047v2 [math.ST] UPDATED)

We propose a goodness-of-fit test for degree-corrected stochastic block
models (DCSBM). The test is based on an adjusted chi-square statistic for
measuring equality of means among groups of $n$ multinomial distributions with
$d_1,\dots,d_n$ observations. In the context of network models, the number of
multinomials, $n$, grows much faster than the number of observations, $d_i$,
corresponding to the degree of node $i$, hence the setting deviates from
classical asymptotics. We show that a simple adjustment allows the statistic to
converge in …

arxiv chi-square math test