Sensitivity Analysis in Fitting Auto- and Cross-Variogram Model

In spatial statistics, prediction method the value at a specified location with data of a single variable is called kriging . It is performed through three stages of (1) estimating variograms, (2) fitting the variogram model to the estimated variograms, and (3) predicting the value at a specified location using the resulting fitted model. It is naturally extended to cokriging , which is performed in the similar three stages when multivariate data are available. In case additional observations of one and more covariables are available, cokriging may lead to increased precision of the prediction. Recently, sensitivity analysis for spatial data takes a growing interest in spatial statistics. An aim of the present article is to propose a method to detect influential observations in the second stage of cokriging . For the present article, we derive influence functions, and then sensitivity analysis is performed using the derived influence functions. The Euclidean norm of the influence functions is used as methods to detect influential observations. A real numerical example is analyzed to show the validity or usefulness of the proposed influence functions.