Analysing positive-valued spatial data: the transformed Gaussian
model
Ole F. Christensen(1), Peter J. Diggle(2) & Paulo J. Ribeiro Jr.(3)
Abstract
The Gaussian
assumption is often inappropriate for analysing some kinds of geostatistical data and transformations can be used in
an attempt to get nearly-Gaussian behaviour. In this paper we study the
transformed Gaussian model, which includes an additional parameter
corresponding to the Box-Cox family of transformations.
In particular we consider maximum
likelihood estimation and minimum mean square error
prediction for this model, and as an example we use it to model rainfall
data. We discuss the limitations of the transformed Gaussian model,
and suggest that it should be used primarily
as a first line of attack in dealing
with non-Gaussianity and non-linearity, before proceding to more
complex models.
Keywords: Box-Cox transformation, geostatistics,
likelihood, non-Gaussian models, rainfall, transformed Gaussian model.
(1) Aalborg University.
Address: Dept. of Mathematical Sciences, Aalborg University, Denmark
e-mail: olefc@math.auc.dk
(2) Lancaster University.
Address: Department of Mathematics and Statistics, Lancaster University, Lancaster LA1-4YF
e-mail: paulojus@est.ufpr.br
(3) Universidade Federal do Paraná and Lancaster University.
Address: Department of Mathematics and Statistics, Lancaster University, Lancaster LA1-4YF
e-mail: paulojus@est.ufpr.br
http://www.maths.lancs.ac.uk/~ribeiro/
Last modified: Tue Oct 24 13:13:01 BST 2000