[R-sig-Geo] Test for spatial stationarity

[Roger Bivand]

On Tue, 1 Aug 2017, sara osama wrote:

> Dear all
> Hope this email finds you well. I want to ask if there is a formal test 
> for spatial stationarity like the one for temporal stationarity.  I have 
> searched a lot, but I could not find a formal test by which we can 
> conclude about stationarity in spatial data.

Sara:

Could you please clarify what you mean by "spatial data"? Do you mean 
point observations of a continuous spatial process - say to make 
predictions for unobserved locations, as in kriging? In this case, there 
is a formal literature discussing stationarity, although I'm not aware of 
formal tests (practically one might compare predictions made using models 
that assume stationarity and those that do not, to see whether the 
assumption changes the output; if it does, probably stationarity is not 
present as assumed).

In the point process literature (point patterns), there are also results, 
but they are often handled by relaxing assumptions about the homogeneity 
of the underlying surface (introducing covariates influencing the 
process).

For lattice (aggregated, polygon) data, there are tests based on 
geographically weighted regression, but these lack power if the bandwidth 
is inappropriate and/or the underlying model is mis-specified. They are 
not univariate tests, and may best be seen as exploratory. There may be 
other literatures, look for work for example by Werner Mueller and 
co-authors.

Hope this helps,

Roger


> I would be grateful if anyone can help me with this.
> Best
> Sara
>
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-- 
Roger Bivand
Department of Economics, Norwegian School of Economics,
Helleveien 30, N-5045 Bergen, Norway.
voice: +47 55 95 93 55; e-mail: Roger.Bivand at nhh.no
Editor-in-Chief of The R Journal, https://journal.r-project.org/index.html
http://orcid.org/0000-0003-2392-6140
https://scholar.google.no/citations?user=AWeghB0AAAAJ&hl=en