Journal Article

Fixed rank kriging for very large spatial data sets

Johannesson, Gardar, Cressie, Noel

2008

Overview

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 [graphic removed] . 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.

• Publisher: Oxford, UK : Blackwell Publishing Ltd,Blackwell Publishing Ltd,Blackwell Publishing,Blackwell,Royal Statistical Society,Oxford University Press
• Subject: Analysis of covariance / Artificial satellites / Atmospheric ozone / Best linear unbiased predictor / Bias / Covariance / Covariance function / Covariance matrices / Data / Data analysis / data collection / Datasets / equations / Estimating techniques / Estimation / Estimators / Exact sciences and technology / Families & family life / Frobenius norm / General topics / Geology / Geostatistics / Inference from stochastic processes; time series analysis / Kriging / Mathematical analysis / Mathematical functions / Mathematics / Mean square errors / Mean-squared prediction error / Measure and integration / Multivariate analysis / Non-stationarity / ozone / prediction / Predictions / Probability and statistics / Remote sensing / Sciences and techniques of general use / Spatial data / Spatial models / Spatial prediction / Standard error / Statistical methods / Statistics / Studies / Total column ozone