  We propose a method for constructing confidence intervals that account for
many forms of spatial correlation. The interval has the familiar `estimator
plus and minus a standard error times a critical value' form, but we propose
new methods for constructing the standard error and the critical value. The
standard error is constructed using population principal components from a
given `worst-case' spatial covariance model. The critical value is chosen to
ensure coverage in a benchmark parametric model for the spatial correlations.
The method is shown to control coverage in large samples whenever the spatial
correlation is weak, i.e., with average pairwise correlations that vanish as
the sample size gets large. We also provide results on correct coverage in a
restricted but nonparametric class of strong spatial correlations, as well as
on the efficiency of the method. In a design calibrated to match economic
activity in U.S. states the method outperforms previous suggestions for
spatially robust inference about the population mean.
