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A note on the correlation structure of transformed Gaussian random fields
Author(s) -
De Oliveira Victor
Publication year - 2003
Publication title -
australian and new zealand journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.434
H-Index - 41
eISSN - 1467-842X
pISSN - 1369-1473
DOI - 10.1111/1467-842x.00289
Subject(s) - random field , mathematics , gaussian random field , gaussian , transformation (genetics) , orthogonality , random function , property (philosophy) , statistical physics , correlation function (quantum field theory) , series (stratigraphy) , scale (ratio) , gaussian process , field (mathematics) , statistics , pure mathematics , geometry , paleontology , biochemistry , physics , chemistry , philosophy , epistemology , spectral density , quantum mechanics , biology , gene
Summary Transformed Gaussian random fields can be used to model continuous time series and spatial data when the Gaussian assumption is not appropriate. The main features of these random fields are specified in a transformed scale, while for modelling and parameter interpretation it is useful to establish connections between these features and those of the random field in the original scale. This paper provides evidence that for many ‘normalizing’ transformations the correlation function of a transformed Gaussian random field is not very dependent on the transformation that is used. Hence many commonly used transformations of correlated data have little effect on the original correlation structure. The property is shown to hold for some kinds of transformed Gaussian random fields, and a statistical explanation based on the concept of parameter orthogonality is provided. The property is also illustrated using two spatial datasets and several ‘normalizing’ transformations. Some consequences of this property for modelling and inference are also discussed.