  Regional data analysis is concerned with the analysis and modeling of
measurements that are spatially separated by specifically accounting for
typical features of such data. Namely, measurements in close proximity tend to
be more similar than the ones further separated. This might hold also true for
cross-dependencies when multivariate spatial data is considered. Often,
scientists are interested in linear transformations of such data which are easy
to interpret and might be used as dimension reduction. Recently, for that
purpose spatial blind source separation (SBSS) was introduced which assumes
that the observed data are formed by a linear mixture of uncorrelated, weakly
stationary random fields. However, in practical applications, it is well-known
that when the spatial domain increases in size the weak stationarity
assumptions can be violated in the sense that the second order dependency is
varying over the domain which leads to non-stationary analysis. In our work we
extend the SBSS model to adjust for these stationarity violations, present
three novel estimators and establish the identifiability and affine
equivariance property of the unmixing matrix functionals defining these
estimators. In an extensive simulation study, we investigate the performance of
our estimators and also show their use in the analysis of a geochemical dataset
which is derived from the GEMAS geochemical mapping project.
