Kernel density estimation for spatial processes: the L1 theory

Authors:
Marc Hallin;Zudi Lu;Lanh T. Tran
Affiliations:
Institut de Statistique et de Recherche Opérationnelle (ISRO) and E.C.A.R.E.S., Université Libre de Bruxelles, Campus de la Plaine and Département de Mathématique, Universit ...;Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing 100080, China;Department of Mathematics, Indiana University, Bloomington, IN
Venue:
Journal of Multivariate Analysis
Year:
2004

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Abstract

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 L1 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.