Tukey g-and-h Random Fields

Ganggang Xu, Marc G. Genton

Research output: Contribution to journalArticlepeer-review

47 Scopus citations

Abstract

We propose a new class of transGaussian random fields named Tukey g-and-h (TGH) random fields to model non-Gaussian spatial data. The proposed TGH random fields have extremely flexible marginal distributions, possibly skewed and/or heavy-tailed, and, therefore, have a wide range of applications. The special formulation of the TGH random field enables an automatic search for the most suitable transformation for the dataset of interest while estimating model parameters. Asymptotic properties of the maximum likelihood estimator and the probabilistic properties of the TGH random fields are investigated. An efficient estimation procedure, based on maximum approximated likelihood, is proposed and an extreme spatial outlier detection algorithm is formulated. Kriging and probabilistic prediction with TGH random fields are developed along with prediction confidence intervals. The predictive performance of TGH random fields is demonstrated through extensive simulation studies and an application to a dataset of total precipitation in the south east of the United States. Supplementary materials for this article are available online.

Original languageEnglish (US)
Pages (from-to)1236-1249
Number of pages14
JournalJournal of the American Statistical Association
Volume112
Issue number519
DOIs
StatePublished - Jul 3 2017
Externally publishedYes

Keywords

  • Heavy tails
  • Kriging
  • Non-Gaussian random field
  • Probabilistic prediction
  • Skewness
  • Spatial outliers

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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