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

This paper considers spatial data z(s1), z(s2), ... , z(sn) collected at n locations, with the objective of predicting z(s0) 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

SPATIAL REGRESSION MODELS USING INTER-REGION DISTANCES IN A NON-RANDOM CONTEXT

April 2000through a variogram or covariance function, and correct estimation of the variogram (or covariance function) is very crucial. The model assumption (Cressie 1991) is Z(s) = + (s) where (s) is a zero mean stochastic term with variogram 2 (). If we assume intrinsic stationarity then E(Z(s + h) ; Z(s)) = 0 and the variogram is de ned as Var(Z(s + h) ; Z(s)) = 2 (h) This can be written as Var(Z(s + h); Z(s)) = E(Z(s + h) ; Z(s)) 2 and thus the method of moments estimator for the variogram can be used (also called the classical estimator, Cressie 1991) 2^(h) =

SPATIAL REGRESSION MODELS USING INTER-REGION DISTANCES IN A NON-RANDOM CONTEXT

This paper considers spatial data z, z(s2), z(sn) collected at n locations, with the objective of predicting z (s0) 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.Statistics Working Papers Serie