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