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Kernel density estimation for spatial processes: the L1 theory


Author Info

  • Marc Hallin
  • Zudi Lu
  • Lanh T. Tran


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.

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Bibliographic Info

Paper provided by ULB -- Universite Libre de Bruxelles in its series ULB Institutional Repository with number 2013/2127.

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Date of creation: 2004
Date of revision:
Publication status: Published in: Journal of Multivariate Analysis (2004) v.88,p.61-75
Handle: RePEc:ulb:ulbeco:2013/2127

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Cited by:
  1. Jenish, Nazgul, 2012. "Nonparametric spatial regression under near-epoch dependence," Journal of Econometrics, Elsevier, Elsevier, vol. 167(1), pages 224-239.
  2. Gao, Jiti & Lu, Zudi & Tjostheim, Dag, 2003. "Estimation in semiparametric spatial regression," MPRA Paper 11971, University Library of Munich, Germany.
  3. Mohamed El Machkouri, 2011. "Asymptotic normality of the Parzen–Rosenblatt density estimator for strongly mixing random fields," Statistical Inference for Stochastic Processes, Springer, Springer, vol. 14(1), pages 73-84, February.
  4. Gao, Jiti & Lu, Zudi & Tjøstheim, Dag, 2008. "Moment inequalities for spatial processes," Statistics & Probability Letters, Elsevier, Elsevier, vol. 78(6), pages 687-697, April.
  5. Nadia Bensaïd & Sophie Dabo-Niang, 2010. "Frequency polygons for continuous random fields," Statistical Inference for Stochastic Processes, Springer, Springer, vol. 13(1), pages 55-80, April.
  6. Peter Robinson, 2008. "Developments in the analysis of spatial data," LSE Research Online Documents on Economics, London School of Economics and Political Science, LSE Library 25473, London School of Economics and Political Science, LSE Library.
  7. Jia Chen & Li-Xin Zhang, 2010. "Local linear M-estimation for spatial processes in fixed-design models," Metrika, Springer, Springer, vol. 71(3), pages 319-340, May.
  8. Liliana Forzani & Ricardo Fraiman & Pamela Llop, 2013. "Density estimation for spatial-temporal models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer, Springer, vol. 22(2), pages 321-342, June.
  9. Jenish, Nazgul & Prucha, Ingmar R., 2012. "On spatial processes and asymptotic inference under near-epoch dependence," Journal of Econometrics, Elsevier, Elsevier, vol. 170(1), pages 178-190.
  10. Sophie Dabo-Niang & Anne-Françoise Yao, 2013. "Kernel spatial density estimation in infinite dimension space," Metrika, Springer, Springer, vol. 76(1), pages 19-52, January.


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