Technical Appendix for: Spatial Correlation Robust Inference with Errors in Location or Distance

Our model assumes a population of agents residing at d-dimensional integer lattice locations with one individual per location. We focus on an expectation zero process Xs indexed on this lattice that is assumed to be mixing as detailed below. For simplicity, we also assume the process is stationary: the joint distribution of Xs for a collection of locations is invariant to translation and so, assuming second moments exist, EfXsXs+hg = C(h): The econometrician’s sample consists of realizations of agents’random variables Xs at a collection of locations fsig inside a sample region and measurements of these locations. We use the notation j j to denote the number of agents in our sample region and, for simplicity, assume that all locations in are sampled. When taking limits, we view as one of a sequence of regions indexed by that grow to include the whole lattice, an increasing domain approach to asymptotic approximations. In what follows, we state the notion of mixing coe¢ cients used throughout this Appendix, and provide proofs of the results in Conley and Molinari (2005).