Nonparametric Network Bootstrap

Résumé

Inference on network data is challenging due to the strong dependence between observations, which renders standard techniques incorrect. To address this, we propose a valid bootstrap procedure for network data based on a nonparametric linking function estimator. We characterise the conditions under which this estimator is uniformly consistent. We prove that the distribution of the bootstrap network is consistent for the distribution of the original network in terms of a Wasserstein distance. We also provide conditions under which distributions of a class of functions related to U-statistics on the bootstrapped networks consistently replicate the distributions of the corresponding statistics on the original network. Monte Carlo simulations show good confidence interval coverage for a wider class of network functions than those accounted for by our theory. We apply our method to the data from Banerjee, Chandrasekhar, Duflo, and Jackson (2013): we replicate their findings, but also show that our method works under weaker assumptions and with a significantly smaller sample size. Finally, we propose an alternative specification of their model which takes advantage of our linking function estimator and may be of interest independently of our bootstrap procedure.