On the Theoretical Properties of the Network Jackknife

Robert Lunde, Qiaohui Lin, Purnamrita Sarkar

Abstract:

We study the properties of a leave-node-out jackknife procedure for network data. Under the
sparse graphon model, we prove an Efron-Steintype 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.