Estimation of a non stationary cov. modelΒΆ
Let be a multivariate
normal process of dimension
where
.
is supposed to be a second order process and we note
its covariance function.
We denote
the vertices of
the common mesh
and
the associated values
of the field
. We suppose that we have
fields.
We recall that the covariance function
writes:
(1)ΒΆ
where the mean function is defined by:
(2)ΒΆ
First, we estimate the covariance function on the
vertices of the mesh
. At each vertex
, we use the empirical mean estimator applied
to the
fields to estimate:
at the vertex
:
(3)ΒΆ
at the vertices
:
(4)ΒΆ
Then, we build a covariance function defined on
which is a piecewise constant function defined
on
by:
where is such that
is the vertex of
the nearest to
and
the
nearest to
.