Spatial Regression Models Using Inter-Region Distances in a Non-Random Context

Abstract

This article considers spatial data z( s ₁), z( s ₂),…, z( s _n ) collected at n locations, with the objective of predicting z( s ₀) at another location. The usual method of analysis for this problem is kriging, but here we introduce a new signal-plus-noise model whose essential feature is the identification of hot spots. The signal decays in relation to distance from hot spots. We show that hot spots can be located with high accuracy and that the decay parameter can be estimated accurately. This new model compares well to kriging in simulations.

Keywords:

• Hot spot
• Kriging
• Spatial prediction
• Variogram

Mathematics Subject Classification:

• Primary 62H11
• Secondary 86A32

Acknowledgments

The authors would like to thank Hongquan Xu, Rick Paik Schoenberg, and two anonymous referees for their helpful comments.