Kernel density estimation for spatial processes: the L1 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 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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|Date of creation:||2004|
|Publication status:||Published in: Journal of Multivariate Analysis (2004) v.88,p.61-75|
|Contact details of provider:|| Postal: CP135, 50, avenue F.D. Roosevelt, 1050 Bruxelles|
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- Tran, Lanh Tat, 1992. "Kernel density estimation for linear processes," Stochastic Processes and their Applications, Elsevier, vol. 41(2), pages 281-296, June.
- Masry, Elias & Györfi, László, 1987. "Strong consistency and rates for recursive probability density estimators of stationary processes," Journal of Multivariate Analysis, Elsevier, vol. 22(1), pages 79-93, June.
- Tran, L. T. & Yakowitz, S., 1993. "Nearest Neighbor Estimators for Random Fields," Journal of Multivariate Analysis, Elsevier, vol. 44(1), pages 23-46, January.
- Marc Hallin & Zudi Lu & Lanh T. Tran, 2001. "Density estimation for spatial linear processes," ULB Institutional Repository 2013/2109, ULB -- Universite Libre de Bruxelles.
- Ioannides, D. & Roussas, G. G., 1987. "Note on the uniform convergence of density estimates for mixing random variables," Statistics & Probability Letters, Elsevier, vol. 5(4), pages 279-285, June.
- Tran, Lanh Tat, 1990. "Kernel density estimation on random fields," Journal of Multivariate Analysis, Elsevier, vol. 34(1), pages 37-53, July.
- Kulkarni, P. M., 1992. "Estimation of parameters of a two-dimensional spatial autoregressive model with regression," Statistics & Probability Letters, Elsevier, vol. 15(2), pages 157-162, September.
- Marc Hallin & Michel Carbon & Lanh T. Tran, 1996. "Kernel density estimation on random fields: the L1 theory," ULB Institutional Repository 2013/2065, ULB -- Universite Libre de Bruxelles.
- Boente, Graciela & Fraiman, Ricardo, 1988. "Consistency of a nonparametric estimate of a density function for dependent variables," Journal of Multivariate Analysis, Elsevier, vol. 25(1), pages 90-99, April.
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