Abstract

Kriging is a well known notion in geostatistics which aim at the construction of optimal prediction for unobserved quantities of interest. In this paper we derive optimal prediction of a second-order stationary spatial process by minimizing the quadratic risk or mean square error of the predictor subject to some additional conditions. The coefficients of the linear predictor are calculated by a formula which is obtained by applying Lagrange method. The spatial process under study is assumed to be isotropic with a variogram model belongs to quadratic family. Least squares estimation to the parameters of the variogram model is calculated by graphical method. The validity of the mean function is investigated by utilizing asymptotic test based on the partial sums process of weighted least squares residuals. The application of the method to spatial process of rate of growth of corn plants results in the kriging map of the process. The maps are generated under two different variogram models: power and linear (Tent) models.

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