Regression and Classification by Zonal Kriging
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Consider a family Z={x_i,y_i,1≤ i≤ N} of N pairs of vectors x_i∈R^d and scalars y_i that we aim to predict for a new sample vector x_0. Kriging models y as a sum of a deterministic function m, a drift which depends on the point x, and a random function z with zero mean. The zonality hypothesis interprets y as a weighted sum of d random functions of a single independent variables, each of which is a kriging, with a quadratic form for the variograms drift. We can therefore construct an unbiased estimator y^*(x_0)=∑_iλ^iz(x_i) de y(x_0) with minimal variance E[y^*(x_0)-y(x_0)]^2, with the help of the known training set points. We give the explicitly closed form for λ^i without having calculated the inverse of the matrices.
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