In Isaaks and Srivastava's Applied Geostatistics (1989), the use of 'de-clustering' weights are described as a method for computing estimates of the mean and variance with data that are clustered geographically.
I would appreciate feedback regarding the theoretical basis for using spatial weights to compute estimates of the mean and (population) variance, and for making inferences regarding population parameters. Through simulation tests, I have some evidence that this method performs fairly well with weights derived from Thiessen polygons for populations with varying degrees of spatial autocorrelation and skewness. However, I am not aware of any theoretical basis/justification for the weights. Intuitively, the use of spatial weights to account for geographic location of the observations (and possibly spatial autocorrelation among the observations) seems analogous to the common practice in survey statistics of adjusting sample weights to correct for non-response, etc, where the objective is to adjust the weights to account for observed differences between some attribute of the observations (e.g., socioeconomic status) and the target population. In the spatial weighting case, the adjustment is to correct for observed geographical clustering. One notable difference is that in many cases, the data that I work with was not collected using random sampling methods. Your feedback would be appreciated. Best regards, Bill
