de Oliveira, Victor A note on the correlation structure of transformed Gaussian random fields. (English) Zbl 1064.62100 Aust. N. Z. J. Stat. 45, No. 3, 353-366 (2003). 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. Cited in 5 Documents MSC: 62M40 Random fields; image analysis 62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH) Keywords:Box-cox family; correlation function; orthogonal parameters; recursive-type function; spatial data PDFBibTeX XMLCite \textit{V. de Oliveira}, Aust. N. Z. J. Stat. 45, No. 3, 353--366 (2003; Zbl 1064.62100) Full Text: DOI