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Density estimation over spatio-temporal data streams

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  • Amiri, Aboubacar
  • Dabo-Niang, Sophie

Abstract

In the last few years, data can be collected extremely easily in many scientific research fields. This became possible by the recent technological advances that have made online monitoring possible. In such situations, if real time or online estimations are expected, the usual nonparametric techniques rapidly require a lot of time to be computed and therefore become useless in practice. Adaptative counterparts of the classical kernel density estimators, that can be updated extremely easily when a new set of observations is available are investigated, for spatio-temporal processes with weak dependence structures. Mean square, uniform almost sure convergences and a central limit result are obtained under general and easily verifiable conditions. The efficiency of the considered estimators is evaluated through simulations and a real data application. The results show that the proposed method works well within the framework of a spatio-temporal data stream.

Suggested Citation

  • Amiri, Aboubacar & Dabo-Niang, Sophie, 2018. "Density estimation over spatio-temporal data streams," Econometrics and Statistics, Elsevier, vol. 5(C), pages 148-170.
    • Handle: RePEc:eee:ecosta:v:5:y:2018:i:c:p:148-170
    DOI: 10.1016/j.ecosta.2017.08.005
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    References listed on IDEAS

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    1. 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.
    2. Han-Ying Liang & Jong-Il Baek, 2004. "Asymptotic normality of recursive density estimates under some dependence assumptions," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 60(2), pages 155-166, September.
    3. Jenish, Nazgul, 2012. "Nonparametric spatial regression under near-epoch dependence," Journal of Econometrics, Elsevier, vol. 167(1), pages 224-239.
    4. István Fazekas & Alexey Chuprunov, 2006. "Asymptotic Normality of Kernel Type Density Estimators for Random Fields," Statistical Inference for Stochastic Processes, Springer, vol. 9(2), pages 161-178, July.
    5. Robinson, P.M., 2011. "Asymptotic theory for nonparametric regression with spatial data," Journal of Econometrics, Elsevier, vol. 165(1), pages 5-19.
    6. Gérard Biau & Benoît Cadre, 2004. "Nonparametric Spatial Prediction," Statistical Inference for Stochastic Processes, Springer, vol. 7(3), pages 327-349, October.
    7. Peter Robinson, 2011. "Asymptotic theory for nonparametric regression with spatial data," CeMMAP working papers CWP11/11, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    8. Carbon, Michel & Tran, Lanh Tat & Wu, Berlin, 1997. "Kernel density estimation for random fields (density estimation for random fields)," Statistics & Probability Letters, Elsevier, vol. 36(2), pages 115-125, December.
    9. Marc Hallin & Zudi Lu & Lanh T. Tran, 2001. "Density estimation for spatial linear processes," ULB Institutional Repository 2013/2109, ULB -- Universite Libre de Bruxelles.
    10. Aboubacar Amiri & Baba Thiam & Thomas Verdebout, 2017. "On the Estimation of the Density of a Directional Data Stream," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 44(1), pages 249-267, March.
    11. Doukhan, Paul & Louhichi, Sana, 1999. "A new weak dependence condition and applications to moment inequalities," Stochastic Processes and their Applications, Elsevier, vol. 84(2), pages 313-342, December.
    12. Paul Doukhan & Sana Louhichi, 2001. "Functional Estimation of a Density Under a New Weak Dependence Condition," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 28(2), pages 325-341, June.
    13. Tran, Lanh Tat, 1990. "Kernel density estimation on random fields," Journal of Multivariate Analysis, Elsevier, vol. 34(1), pages 37-53, July.
    14. Hongxia Wang & Jinde Wang, 2009. "Estimation of the trend function for spatio-temporal models," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 21(5), pages 567-588.
    15. Zudi Lu & Dag Tjøstheim, 2014. "Nonparametric Estimation of Probability Density Functions for Irregularly Observed Spatial Data," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(508), pages 1546-1564, December.
    16. 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.
    17. Eunju Hwang & Dong Shin, 2016. "Kernel estimators of mode under $$\psi $$ ψ -weak dependence," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 68(2), pages 301-327, April.
    18. Marc Hallin & Zudi Lu & Lanh T. Tran, 2004. "Local linear spatial regression," ULB Institutional Repository 2013/2131, ULB -- Universite Libre de Bruxelles.
    19. Christopher K. Wikle & Scott H. Holan, 2015. "Comment," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(511), pages 901-903, September.
    20. Al-Sulami, Dawlah & Jiang, Zhenyu & Lu, Zudi & Zhu, Jun, 2017. "Estimation for semiparametric nonlinear regression of irregularly located spatial time-series data," Econometrics and Statistics, Elsevier, vol. 2(C), pages 22-35.
    21. Hongxia Wang & Jinde Wang & Bo Huang, 2012. "Prediction for spatio-temporal models with autoregression in errors," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 24(1), pages 217-244.
    22. Conley, T. G., 1999. "GMM estimation with cross sectional dependence," Journal of Econometrics, Elsevier, vol. 92(1), pages 1-45, September.
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    1. Gao, Min & Yang, Wenzhi & Wu, Shipeng & Yu, Wei, 2022. "Asymptotic normality of residual density estimator in stationary and explosive autoregressive models," Computational Statistics & Data Analysis, Elsevier, vol. 175(C).

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