Kernel density estimation for spatial processes: the <f>L1</f> theory

The purpose of this paper is to investigate kernel density estimators for spatial processes with linear or nonlinear structures. Sufficient conditions for such estimators to converge in <f>L1</f> are obtained under extremely general, verifiable conditions. The results hold for mixing as well as for nonmixing processes. Potential applications include testing for spatial interaction, the spatial analysis of causality structures, the definition of leading/lagging sites, the construction of clusters of comoving sites, etc. [Copyright &y& Elsevier]