  Increasingly, there is a marked interest in estimating causal effects under
network interference due to the fact that interference manifests naturally in
networked experiments. However, network information generally is available only
up to some level of error. We study the propagation of such errors to
estimators of average causal effects under network interference. Specifically,
assuming a four-level exposure model and Bernoulli random assignment of
treatment, we characterize the impact of network noise on the bias and variance
of standard estimators in homogeneous and inhomogeneous networks. In addition,
we propose method-of-moments estimators for bias reduction where a minimal
number of network replicates are available. We show our estimators are
asymptotically normal and provide confidence intervals for quantifying the
uncertainty in these estimates. We illustrate the practical performance of our
estimators through simulation studies in British secondary school contact
networks.
