Tukey g-and-h Random Fields
نویسندگان
چکیده
We propose a new class of trans-Gaussian 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. Some key words: Continuous Rank Probability Score; Heavy tails; Kriging; LogGaussian random field; Non-Gaussian random field; PIT; Probabilistic prediction; Skewness; Spatial outliers; Spatial statistics; Tukey g-and-h distribution. Short title: Tukey g-and-h Random Fields Department of Mathematical Sciences, Binghamton University, Binghamton, NY 13902, USA. E-mail: [email protected] CEMSE Division, King Abdullah University of Science and Technology, Thuwal 23955-6900, Saudi Arabia. E-mail: [email protected] This research was supported by the King Abdullah University of Science and Technology (KAUST).
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