  Consider a family $Z=\{\boldsymbol{x_{i}},y_{i}$,$1\leq i\leq N\}$ of $N$
pairs of vectors $\boldsymbol{x_{i}} \in \mathbb{R}^d$ and scalars $y_{i}$ that
we aim to predict for a new sample vector $\mathbf{x}_0$. Kriging models $y$ as
a sum of a deterministic function $m$, a drift which depends on the point
$\boldsymbol{x}$, 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
$y^{*}(\boldsymbol{x_{0}})=\sum_{i}\lambda^{i}z(\boldsymbol{x_{i}})$ de
$y(\boldsymbol{x_{0}})$ with minimal variance
$E[y^{*}(\boldsymbol{x_{0}})-y(\boldsymbol{x_{0}})]^{2}$, with the help of the
known training set points. We give the explicitly closed form for $\lambda^{i}$
without having calculated the inverse of the matrices.
