Campus Units
Statistics
Document Type
Article
Publication Version
Submitted Manuscript
Publication Date
2020
Journal or Book Title
arXiv
Abstract
Spatial prediction is commonly achieved under the assumption of a Gaussian random field (GRF) by obtaining maximum likelihood estimates of parameters, and then using the kriging equations to arrive at predicted values. For massive datasets, fixed rank kriging using the Expectation-Maximization (EM) algorithm for estimation has been proposed as an alternative to the usual but computationally prohibitive kriging method. The method reduces computation cost of estimation by redefining the spatial process as a linear combination of basis functions and spatial random effects. A disadvantage of this method is that it imposes constraints on the relationship between the observed locations and the knots. We develop an alternative method that utilizes the Spatial Mixed Effects (SME) model, but allows for additional flexibility by estimating the range of the spatial dependence between the observations and the knots via an Alternating Expectation Conditional Maximization (AECM) algorithm. Experiments show that our methodology improves estimation without sacrificing prediction accuracy while also minimizing the additional computational burden of extra parameter estimation. The methodology is applied to a temperature data set archived by the United States National Climate Data Center, with improved results over previous methodology.
Copyright Owner
The Author(s)
Copyright Date
2020
Language
en
File Format
application/pdf
Recommended Citation
Pazdernik, Karl T. and Maitra, Ranjan, "Estimating basis functions in massive fields under the spatial random effects model" (2020). Statistics Publications. 304.
https://lib.dr.iastate.edu/stat_las_pubs/304
Comments
This is a pre-print of the article Pazdernik, Karl T., and Ranjan Maitra. "Estimating Basis Functions in Massive Fields under the Spatial Mixed Effects Model." arXiv preprint arXiv:2003.05990 (2020). Posted with permission.