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Kernel density estimation for spatial processes: the L1 theory |
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| Authors: | Marc Hallin Zudi Lu Lanh T. Tran |
| Affiliation: | a Institut de Statistique et de Recherche Opérationnelle (ISRO) and E.C.A.R.E.S., Université Libre de Bruxelles, Campus de la Plaine, CP 210, B-1050 Brussels, Belgium b Département de Mathématique, Université Libre de Bruxelles, Campus de la Plaine, CP 320, B-1050 Brussels, Belgium c Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing 100080, China d Department of Mathematics, Indiana University, Bloomington, IN 47405, USA |
| 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. |
| Keywords: | primary 62G07 62G20 secondary 62M10 |
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