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An Efficient Nonparametric Estimate for Spatially Correlated Functional Data


Functional data are often generated by modern biomedical technologies where features related to the pathophysiology and pathogenesis of a disease are interrogated repeatedly over time and at multiple spatially interdependent regions. To reduce model complexity and simplify the resulting inference, possible spatial correlation among neighboring regions is often neglected. In this article, we propose a weighted kernel smoothing estimate of the mean function that leverages the spatial and temporal correlation. We also address the companion problem of developing a simultaneous prediction method for individual curves using discrete samples. We establish the asymptotic properties of the proposed estimate, including its unique maximum efficiency achieving minimum asymptotic variance. The proposed method improves estimation and prediction in the presence of sparse observations, and therefore, is advantageous to biomedical applications that utilize markers to identify features intrinsic to a particular disease at multiple interdependent sites within an organ. Our simulation and case studies show that the proposed method outperforms conventional approaches for characterizing the dynamic functional imaging data, with the maximum benefit achieved in the presence of a small number of repeated scans.

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This research was partially supported by NIH/NCI 5 P30 CA013696 Columbia University CCSG. KAD is partially supported by NIH/NCI CCSG Grant P30CA016672, EDRN Grant U24CA086368-19, SPORE Grant P50CA140388-08, CCTS Grant 5UL1TR000371-07, CPRIT Grants RP150006 and RP160693, MD Anderson Moonshot programs 710499-80-111529-19, 710499-80-116550-21, 710499-80-111995-21.

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Correspondence to Yuan Wang.

Electronic supplementary material

Below is the link to the electronic supplementary material.

Supplementary Materials:

The online supplementary materials include the proofs for Theorem 1-4, implementation of the hierarchical model in Baladandayuthapani et al. [1], empirical investigation for consistency of the spatial correlation parameter and noise variance. (pdf 270KB)

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Wang, Y., Hu, J., Do, KA. et al. An Efficient Nonparametric Estimate for Spatially Correlated Functional Data. Stat Biosci 11, 162–183 (2019).

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  • Local polynomial regression
  • Asymptotic distribution
  • Spatial–temporal correlation
  • Perfusion imaging