Filtered Kriging for Spatial Data with Heterogeneous Measurement Error Variances
Article first published online: 1 MAR 2011
© 2011, The International Biometric Society
Volume 67, Issue 3, pages 947–957, September 2011
How to Cite
Christensen, W. F. (2011), Filtered Kriging for Spatial Data with Heterogeneous Measurement Error Variances. Biometrics, 67: 947–957. doi: 10.1111/j.1541-0420.2011.01563.x
- Issue published online: 14 SEP 2011
- Article first published online: 1 MAR 2011
- Received June 2009. Revised August 2010. Accepted October 2010.
- Heterogeneous variance measurement-error-filtered kriging;
- Spatial prediction;
- Spatial smoothing
Summary When predicting values for the measurement-error-free component of an observed spatial process, it is generally assumed that the process has a common measurement error variance. However, it is often the case that each measurement in a spatial data set has a known, site-specific measurement error variance, rendering the observed process nonstationary. We present a simple approach for estimating the semivariogram of the unobservable measurement-error-free process using a bias adjustment of the classical semivariogram formula. We then develop a new kriging predictor that filters the measurement errors. For scenarios where each site's measurement error variance is a function of the process of interest, we recommend an approach that also uses a variance-stabilizing transformation. The properties of the heterogeneous variance measurement-error-filtered kriging (HFK) predictor and variance-stabilized HFK predictor, and the improvement of these approaches over standard measurement-error-filtered kriging are demonstrated using simulation. The approach is illustrated with climate model output from the Hudson Strait area in northern Canada. In the illustration, locations with high or low measurement error variances are appropriately down- or upweighted in the prediction of the underlying process, yielding a realistically smooth picture of the phenomenon of interest.