Parametric Variogram Matrices Spanning from Weak to Intrinsic Stationarity

• Activity Number: 678 - New Methods in Spatial and Spatiotemporal Modeling and Assessment
• Type: Contributed
• Date/Time: Thursday, August 2, 2018 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistics and the Environment
• Author(s): Wanfang Chen* and Marc G Genton
• Companies: KAUST and King Abdullah University of Science and Technology
• Keywords: bounded and unbounded variogram; cross-variogram; variogram; weak stationarity; intrinsic stationarity; variogram matrix

Abstract

Variogram matrices are important tools in geostatistics for multivariate spatial prediction, also called cokriging. When it is unclear whether the multivariate random field is jointly weakly stationary or jointly intrinsically stationary, a variogram matrix model that is capable of spanning from one to the other is advantageous. We propose several such parametric models for both traditional and pseudo variogram matrices based on the method of latent dimensions and the linear model of coregionalization. Specifically, the entries in the parametric variogram matrix, i.e., the marginal variograms in the diagonal and cross-variograms in the off-diagonals, are able to vary between boundedness and unboundedness by changing the values of parameters.