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Functional Principal Component Analysis of Spatiotemporal Point Processes With Applications in Disease Surveillance

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  • Yehua Li
  • Yongtao Guan

Abstract

In disease surveillance applications, the disease events are modeled by spatiotemporal point processes. We propose a new class of semiparametric generalized linear mixed model for such data, where the event rate is related to some known risk factors and some unknown latent random effects. We model the latent spatiotemporal process as spatially correlated functional data, and propose Poisson maximum likelihood and composite likelihood methods based on spline approximations to estimate the mean and covariance functions of the latent process. By performing functional principal component analysis to the latent process, we can better understand the correlation structure in the point process. We also propose an empirical Bayes method to predict the latent spatial random effects, which can help highlight hot areas with unusually high event rates. Under an increasing domain and increasing knots asymptotic framework, we establish the asymptotic distribution for the parametric components in the model and the asymptotic convergence rates for the functional principal component estimators. We illustrate the methodology through a simulation study and an application to the Connecticut Tumor Registry data. Supplementary materials for this article are available online.

Suggested Citation

  • Yehua Li & Yongtao Guan, 2014. "Functional Principal Component Analysis of Spatiotemporal Point Processes With Applications in Disease Surveillance," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(507), pages 1205-1215, September.
  • Handle: RePEc:taf:jnlasa:v:109:y:2014:i:507:p:1205-1215
    DOI: 10.1080/01621459.2014.885434
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    Cited by:

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    3. Giraldo, Ramón & Dabo-Niang, Sophie & Martínez, Sergio, 2018. "Statistical modeling of spatial big data: An approach from a functional data analysis perspective," Statistics & Probability Letters, Elsevier, vol. 136(C), pages 126-129.
    4. Jiří Dvořák & Michaela Prokešová, 2016. "Parameter Estimation for Inhomogeneous Space-Time Shot-Noise Cox Point Processes," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 43(4), pages 939-961, December.
    5. Li, Yehua & Qiu, Yumou & Xu, Yuhang, 2022. "From multivariate to functional data analysis: Fundamentals, recent developments, and emerging areas," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
    6. Haozhe Zhang & Yehua Li, 2020. "Unified Principal Component Analysis for Sparse and Dense Functional Data under Spatial Dependency," Papers 2006.13489, arXiv.org, revised Jun 2021.
    7. Shirun Shen & Huiya Zhou & Kejun He & Lan Zhou, 2024. "Principal Component Analysis of Two-dimensional Functional Data with Serial Correlation," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 29(3), pages 601-620, September.
    8. Song, Jun & Li, Bing, 2021. "Nonlinear and additive principal component analysis for functional data," Journal of Multivariate Analysis, Elsevier, vol. 181(C).
    9. Anestis Antoniadis & Jean-Michel Poggi, 2015. "Discussion of “Analysis of spatio-temporal mobile phone data: a case study in the metropolitan area of Milan”," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 24(2), pages 307-312, July.

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