Weighted classical variogram estimation for data with clustering

The classical variogram estimate is convenient but can be unacceptable variable. Improved estimators are possible, especially when the locations of the available data are highly clustered. Using a simple theoretical example, we demonstrate that weighting can dramatically increase the efficiency of classical variogram estimates from clustered data. We give expressions for the weights that lead to minimal variance estimators and indicate some obstacles to the use of these weights, We then introduce a simple iterative weighting scheme intended to approximate optimal weighting. We apply the new weighting to the example that motivated this research-estimating the variogram of home radon levels-and demonstrate its performance in a simulation study.