Filtered Kriging for Spatial Data with Heterogeneous Measurement Error Variances

• Activity Number: 16
• Type: Topic Contributed
• Date/Time: Sunday, July 31, 2011 : 2:00 PM to 3:50 PM
• Sponsor: Section on Statistics and the Environment
• Author(s): William F. Christensen*+
• Companies: Brigham Young University
• Keywords: heterogeneous variance measurement error filtered kriging ; HFK ; spatial smoothing ; spatial prediction ; NARCCAP

Abstract

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 which 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 which 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.