SENSITIVITY ANALYSIS IN SPATIAL STATISTICS: DETECTING INFLUENTIAL OBSERVATIONS IN SPATIAL PREDICTION

An important problem in spatial statistics is to predict the unobserved value z(s0) at a specified location s0 based on the information of n observations z(sα), α=1, …, n. It can be achieved in three stages of (1) estimating the variograms, (2) fitting a model to the estimated variograms, and (3) applying the so-called ordinary (or universal) kriging. The present article proposes a method to detect influential observations in variogram estimation, variogram model fitting to the estimated variograms, and spatial prediction using the fitted variogram model. To do this, we derive the influence functions for statistics in the above three stages assuming that the underlying process of the observed spatial data is second-order stationary. A real numerical example is analyzed to show the validity or usefulness of the proposed influence functions. Comparison is made with the influence function derived by Gunst and Hartfield (1997).