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Estimation of the trend function for spatio-temporal models

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  • Hongxia Wang
  • Jinde Wang

Abstract

Spatiotemporal models have been applied in several scientific disciplines. A crucial problem is estimation of the trend function. Although nonparametric regression for spatial data has been studied in many papers, it is not the case for spatio-temporal data. In this article, we propose a local linear fitting method for spatio-temporal data and investigate the problem under what conditions the proposed method can work well. To guarantee the uniformly weakly consistent and asymptotically normal properties, it is just required that at a fixed location i0, {R(i0, t), t∈Tn} is strictly stationary, at a fixed moment t0, {R(i, t0), i∈Λn} is strictly stationary which is weaker than {R(i, t), i∈Λn, t∈Tn} is strictly stationary both in time and space locations. This assumption can be met often in practice, and the proposed estimation method can be applied widely. The simulation results and case study show that the estimator performs well.

Suggested Citation

  • 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.
    • Handle: RePEc:taf:gnstxx:v:21:y:2009:i:5:p:567-588
    DOI: 10.1080/10485250902783608
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    References listed on IDEAS

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    1. Mohamed Machkouri, 2007. "Nonparametric Regression Estimation for Random Fields in a Fixed-Design," Statistical Inference for Stochastic Processes, Springer, vol. 10(1), pages 29-47, January.
    2. Gérard Biau & Benoît Cadre, 2004. "Nonparametric Spatial Prediction," Statistical Inference for Stochastic Processes, Springer, vol. 7(3), pages 327-349, October.
    3. 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.
    4. Hall, Peter & Hart, Jeffrey D., 1990. "Nonparametric regression with long-range dependence," Stochastic Processes and their Applications, Elsevier, vol. 36(2), pages 339-351, December.
    5. Tran, Lanh Tat, 1990. "Kernel density estimation on random fields," Journal of Multivariate Analysis, Elsevier, vol. 34(1), pages 37-53, July.
    6. Lu, Zudi & Chen, Xing, 2004. "Spatial kernel regression estimation: weak consistency," Statistics & Probability Letters, Elsevier, vol. 68(2), pages 125-136, June.
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    Cited by:

    1. Hongxia Wang & Zihan Zhao & Hongxia Hao & Chao Huang, 2023. "Estimation and Inference for Spatio-Temporal Single-Index Models," Mathematics, MDPI, vol. 11(20), pages 1-32, October.
    2. Amiri, Aboubacar & Dabo-Niang, Sophie, 2018. "Density estimation over spatio-temporal data streams," Econometrics and Statistics, Elsevier, vol. 5(C), pages 148-170.
    3. Bastian Schäfer, 2021. "Bandwidth selection for the Local Polynomial Double Conditional Smoothing under Spatial ARMA Errors," Working Papers CIE 146, Paderborn University, CIE Center for International Economics.
    4. S.‐H. Arnaud Kanga & Ouagnina Hili & Sophie Dabo‐Niang & Assi N'Guessan, 2023. "Asymptotic properties of nonparametric quantile estimation with spatial dependency," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 77(3), pages 254-283, August.
    5. 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.

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