Regression and Classification by Zonal Kriging

Abstract

Consider a family Z= _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)=_i^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 ^i without having calculated the inverse of the matrices.

Tasks

Reproductions