Qiaohui Lin

Qiaohui Lin, Robert Lunde, Purnamrita Sarkar

We propose a new class of multiplier bootstraps for count functionals, ranging from a fast, approximate linear bootstrap tailored to sparse, massive graphs to a quadratic bootstrap procedure that offers refined accuracy for smaller, denser graphs. For the fast, approximate linear bootstrap, we show that $\sqrt{n}$-consistent inference of the count functional is attainable in certain computational regimes that depend on the sparsity level of the graph. Furthermore, even in more challenging regimes, we prove that our bootstrap procedure offers valid coverage and vanishing confidence intervals. For the quadratic bootstrap, we establish an Edgeworth expansion and show that this procedure offers higher-order accuracy under appropriate sparsity conditions. We complement our theoretical results with a simulation study and real data analysis and verify that our procedure offers state-of-the-art performance for several functionals.

Qiaohui Lin, Robert Lunde, Purnamrita Sarkar

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.