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A three-step local smoothing approach for estimating the mean and covariance functions of spatio-temporal Data

Author

Listed:
  • Kai Yang

    (University of Florida)

  • Peihua Qiu

    (University of Florida)

Abstract

Spatio-temporal data are common in practice. Existing methods for analyzing such data often employ parametric modelling with different sets of model assumptions. However, spatio-temporal data in practice often have complicated structures, including complex spatial and temporal data variation, latent spatio-temporal data correlation, and unknown data distribution. Because such data structures reflect the complicated impact of confounding variables, such as weather, demographic variables, life styles, and other cultural and environmental factors, they are usually too complicated to describe by parametric models. In this paper, we suggest a general modelling framework for estimating the mean and covariance functions of spatio-temporal data using a three-step local smoothing procedure. The suggested method can well accommodate the complicated structure of real spatio-temporal data. Under some regularity conditions, the consistency of the proposed estimators is established. Both simulation studies and a real-data application show that our proposed method could work well in practice.

Suggested Citation

  • Kai Yang & Peihua Qiu, 2022. "A three-step local smoothing approach for estimating the mean and covariance functions of spatio-temporal Data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 74(1), pages 49-68, February.
    • Handle: RePEc:spr:aistmt:v:74:y:2022:i:1:d:10.1007_s10463-021-00787-2
    DOI: 10.1007/s10463-021-00787-2
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    References listed on IDEAS

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    1. Michael Vogt & Oliver Linton, 2014. "Nonparametric estimation of a periodic sequence in the presence of a smooth trend," Biometrika, Biometrika Trust, vol. 101(1), pages 121-140.
    2. Jonathan R. Stroud & Peter Müller & Bruno Sansó, 2001. "Dynamic models for spatiotemporal data," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(4), pages 673-689.
    3. Thaís C. O. Fonseca & Mark F. J. Steel, 2011. "Non-Gaussian spatiotemporal modelling through scale mixing," Biometrika, Biometrika Trust, vol. 98(4), pages 761-774.
    4. Lyndsay Shand & Bo Li, 2017. "Modeling nonstationarity in space and time," Biometrics, The International Biometric Society, vol. 73(3), pages 759-768, September.
    5. Christopher Wikle & Mevin Hooten, 2010. "Rejoinder on: A general science-based framework for dynamical spatio-temporal models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 19(3), pages 466-468, November.
    6. Taylor, Benjamin M. & Davies, Tilman M. & Rowlingson, Barry S. & Diggle, Peter J., 2015. "Bayesian Inference and Data Augmentation Schemes for Spatial, Spatiotemporal and Multivariate Log-Gaussian Cox Processes in R," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 63(i07).
    7. Christopher Wikle & Mevin Hooten, 2010. "A general science-based framework for dynamical spatio-temporal models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 19(3), pages 417-451, November.
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