LAUSR

www.stat.wisc.edu UW-Department of Statistics (608) 262-2598 We develop a general framework for conducting inference with linear unbiased estimators given constraints on observations' independence relations, in the form of a dependency graph. We establish the consistency of an oracle variance estimator when the dependency graph is known, along with an associated central limit theorem. We derive an integer linear program for finding an upper bound for the estimated variance when the dependency graph is unknown, but topological or degree-based constraints are available. We develop alternative bounds, including a closed-form bound, under an additional homoskedasticity assumption. We establish a basis for Wald-type confidence intervals that are guaranteed to have asymptotically conservative coverage. We apply the approach to inference from a social network link-tracing study and provide statistical software implementing the approach.