Fixed Rank Kriging for Very Large Spatial Data Sets

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ID: 299460
2008
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Ranked #127 of 145 articles by views in Journal of the Royal Statistical Society Series B (Statistical Methodology)

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Abstract
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 n3. 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.
Reference Key
openalex_W1524392826 Use this key to autocite in the manuscript while using SciMatic Manuscript Manager or Thesis Manager
Authors Noel Cressie, Gardar Johannesson
Journal Journal of the Royal Statistical Society Series B (Statistical Methodology)
Year 2008
DOI
10.1111/j.1467-9868.2007.00633.x
URL
https://doi.org/10.1111/j.1467-9868.2007.00633.x
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