Bootstrapping of Spatially Correlated Data

The application of the bootstrap to spatially correlated data has not been studied as widely as its application to time series data. This is a challenging problem since it is difficult to preserve the correlation structure of the data while implementing the bootstrap method. Kunsch (1989), Politis and Romano(1993, Liu and Singh(1992) have suggested bootstrapping methods for higher dimensional data. We are proposing a new bootstrapping method for spatial data and are studying the properties of the estimators for the mean and the semi-variogram under our method. We demonstrate the performance and usefulness of this method by a simulation study. We will also show consistency and derive asymptotic distributional properties of the estimators. As an applicaiton we are studying the problem of modeling shoreline erosion along the coast of North Carolina and we apply our method in an effort to model the underlying correlation structure and build a complete model for the shoreline erosion process.