Kriging
Chapter 4 discusses kriging; one calls kriging, or simple kriging, of the random function Y in a panel P the best linear estimator Y K of Y by N samples Y α. This optimum is given by starting from the extension variance of Y − Y K, where Y K = λ α Y α, and by calculating its minimum with respect to the λ α upon the condition that the sum of these coefficients equals 1 (the non-bias condition). This results in the kriging equations, that is, a Lagrange linear system of equations in λ α. When the panel P reduces to one point x moving into the space, then the kriging yields the best estimation map of the random function Y. The approach extends to the case when the samples form a continuous set. In dimension 1, the kriging system can be formally calculated, and the corresponding expressions are given for linear variograms and de Wijsian variograms.