On the Theoretical Properties of the Network Jackknife
This work addresses variance estimation in network analysis, offering a method that is theoretically validated and practically useful for researchers in statistics and data science, though it is incremental as it builds on existing jackknife techniques.
The paper tackles the problem of estimating variance for network functionals by proposing a leave-node-out jackknife procedure, proving it yields conservative variance estimates under the sparse graphon model and showing competitive performance in simulations and real data, with the jackknife providing more accurate inferences than subsampling for several network statistics.
We study the properties of a leave-node-out jackknife procedure for network data. Under the sparse graphon model, we prove an Efron-Stein-type inequality, showing that the network jackknife leads to conservative estimates of the variance (in expectation) for any network functional that is invariant to node permutation. For a general class of count functionals, we also establish consistency of the network jackknife. We complement our theoretical analysis with a range of simulated and real-data examples and show that the network jackknife offers competitive performance in cases where other resampling methods are known to be valid. In fact, for several network statistics, we see that the jackknife provides more accurate inferences compared to related methods such as subsampling.