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Fixed rank kriging for very large spatial data sets
Author(s) -
Cressie Noel,
Johannesson Gardar
Publication year - 2008
Publication title -
journal of the royal statistical society: series b (statistical methodology)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 6.523
H-Index - 137
eISSN - 1467-9868
pISSN - 1369-7412
DOI - 10.1111/j.1467-9868.2007.00633.x
Subject(s) - kriging , covariance function , covariance , mathematics , spatial analysis , estimator , variogram , data set , rank (graph theory) , statistics , mathematical optimization , algorithm , combinatorics
Summary. Spatial statistics for very large spatial data sets is challenging. The size of the data set, n , causes problems in computing optimal spatial predictors such as kriging, since its computational cost is of order . In addition, a large data set is often defined on a large spatial domain, so the spatial process of interest typically exhibits non‐stationary behaviour over that domain. A flexible family of non‐stationary covariance functions is defined by using a set of basis functions that is fixed in number, which leads to a spatial prediction method that we call fixed rank kriging. Specifically, fixed rank kriging is kriging within this class of non‐stationary covariance functions. It relies on computational simplifications when n is very large, for obtaining the spatial best linear unbiased predictor and its mean‐squared prediction error for a hidden spatial process. A method based on minimizing a weighted Frobenius norm yields best estimators of the covariance function parameters, which are then substituted into the fixed rank kriging equations. The new methodology is applied to a very large data set of total column ozone data, observed over the entire globe, where n is of the order of hundreds of thousands.