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Kernel density estimation for spatial processes: the L1 theory

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  • Hallin, Marc
  • Lu, Zudi
  • Tran, Lanh T.

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.

Suggested Citation

  • Hallin, Marc & Lu, Zudi & Tran, Lanh T., 2004. "Kernel density estimation for spatial processes: the L1 theory," Journal of Multivariate Analysis, Elsevier, vol. 88(1), pages 61-75, January.
    • Handle: RePEc:eee:jmvana:v:88:y:2004:i:1:p:61-75
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    References listed on IDEAS

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    Cited by:

    1. Jenish, Nazgul, 2012. "Nonparametric spatial regression under near-epoch dependence," Journal of Econometrics, Elsevier, vol. 167(1), pages 224-239.
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    3. Kuangyu Wen & Ximing Wu & David J. Leatham, 2021. "Spatially Smoothed Kernel Densities with Application to Crop Yield Distributions," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 26(3), pages 349-366, September.
    4. Jia Chen & Li-Xin Zhang, 2010. "Local linear M-estimation for spatial processes in fixed-design models," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 71(3), pages 319-340, May.
    5. Chang, Yoosoon & Kaufmann, Robert K. & Kim, Chang Sik & Miller, J. Isaac & Park, Joon Y. & Park, Sungkeun, 2020. "Evaluating trends in time series of distributions: A spatial fingerprint of human effects on climate," Journal of Econometrics, Elsevier, vol. 214(1), pages 274-294.
    6. Amiri, Aboubacar & Dabo-Niang, Sophie, 2018. "Density estimation over spatio-temporal data streams," Econometrics and Statistics, Elsevier, vol. 5(C), pages 148-170.
    7. Sophie Dabo-Niang & Anne-Françoise Yao, 2013. "Kernel spatial density estimation in infinite dimension space," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 76(1), pages 19-52, January.
    8. Michel Harel & Jean-François Lenain & Joseph Ngatchou-Wandji, 2016. "Asymptotic behaviour of binned kernel density estimators for locally non-stationary random fields," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 28(2), pages 296-321, June.
    9. Lu, Zudi & Lundervold, Arvid & Tjøstheim, Dag & Yao, Qiwei, 2007. "Exploring spatial nonlinearity using additive approximation," LSE Research Online Documents on Economics 5401, London School of Economics and Political Science, LSE Library.
    10. Nadia Bensaïd & Sophie Dabo-Niang, 2010. "Frequency polygons for continuous random fields," Statistical Inference for Stochastic Processes, Springer, vol. 13(1), pages 55-80, April.
    11. 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;Sociedad de Estadística e Investigación Operativa, vol. 22(2), pages 321-342, June.
    12. Peter M Robinson, 2009. "Developments in the Analysis of Spatial Data," STICERD - Econometrics Paper Series 531, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    13. Rongrong Xu & Jinde Wang, 2008. "-estimation for spatial nonparametric regression," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 20(6), pages 523-537.
    14. Robinson, P.M., 2011. "Asymptotic theory for nonparametric regression with spatial data," Journal of Econometrics, Elsevier, vol. 165(1), pages 5-19.
    15. Zhenyu Jiang & Nengxiang Ling & Zudi Lu & Dag Tj⊘stheim & Qiang Zhang, 2020. "On bandwidth choice for spatial data density estimation," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 82(3), pages 817-840, July.
    16. Tang Qingguo, 2015. "Robust estimation for spatial semiparametric varying coefficient partially linear regression," Statistical Papers, Springer, vol. 56(4), pages 1137-1161, November.
    17. Linwang Yuan & Zhaoyuan Yu & Lin Yi & Wen Luo & Shaofei Chen, 2014. "Multiscale Spatial Decomposition for Skew-Distributed Data with Parallel Spatial Kernel Smoothing," Environment and Planning B, , vol. 41(4), pages 613-636, August.
    18. Jenish, Nazgul & Prucha, Ingmar R., 2012. "On spatial processes and asymptotic inference under near-epoch dependence," Journal of Econometrics, Elsevier, vol. 170(1), pages 178-190.
    19. Tang Qingguo, 2013. "B-spline estimation for semiparametric varying-coefficient partially linear regression with spatial data," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 25(2), pages 361-378, June.
    20. Mohamed El Machkouri, 2011. "Asymptotic normality of the Parzen–Rosenblatt density estimator for strongly mixing random fields," Statistical Inference for Stochastic Processes, Springer, vol. 14(1), pages 73-84, February.
    21. Zudi Lu & Dag Johan Steinskog & Dag Tjøstheim & Qiwei Yao, 2009. "Adaptively varying‐coefficient spatiotemporal models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(4), pages 859-880, September.
    22. Zhang, Rongmao & Chan, Ngai Hang & Chi, Changxiong, 2023. "Nonparametric testing for the specification of spatial trend functions," Journal of Multivariate Analysis, Elsevier, vol. 196(C).
    23. Gao, Jiti & Lu, Zudi & Tjøstheim, Dag, 2008. "Moment inequalities for spatial processes," Statistics & Probability Letters, Elsevier, vol. 78(6), pages 687-697, April.
    24. Zhengyan Lin & Degui Li & Jiti Gao, 2009. "Local Linear M‐estimation in non‐parametric spatial regression," Journal of Time Series Analysis, Wiley Blackwell, vol. 30(3), pages 286-314, May.
    25. Robinson, Peter, 2008. "Developments in the analysis of spatial data," LSE Research Online Documents on Economics 25473, London School of Economics and Political Science, LSE Library.

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