Spatial residual processes and boundary detection : theory and methods

Abstract

Set indexed partial sums of regression residuals obtained from the fit of a regression model to spatial data are used to define the spatial residual process. Limit processes are obtained for these partial sum sets. Statistics are derived for testing a spatial array of observations from a regression model for no change in parameters against possible alternatives involving change of parameters at unknown boundaries. These test statistics are defined in terms of set indexed partial sums, and distributional results based on properties of spatial residual processes are obtained for selected change-boundary statistics. Estimation of the locations of boundaries separating spatial sets of observations is discussed. This methodology is then applied to two sets of data.